# Selina Concise Solutions for Chapter 8 Profit, Loss and Discount Class 8 ICSE Mathematics

### Exercise 8A

**1. Megha bought 10 note-books for Rs.40 and sold them at Rs.4.75 per note-book. Find, her gain percent.**

**Solution**

C.P. of 10 note-books = Rs. 40

S.P. of 10 note-books@ Rs. 4.75 per note-book

= 4.75 × 10

= Rs. 47.50

Gain = S.P. – C.P.

= Rs 47.50 – Rs 40 = Rs 7.50

Gain% = Gain/C.P. × 100

= 7.50/40 × 100

= 750/40%

= 75/4%

= 18 3/4%

**2. A fruit-seller buys oranges at 4 for Rs.3 and sells them at 3 for Rs.4 Find his profit percent.**

**Solution**

Let number of oranges bought = 12

[

**Note:**L.C.M. of 4 and 3 = 12]

∴ C.P. of oranges = Rs. ¾ × 12 = Rs. 9

And S.P. of oranges = Rs. 4/3 × 12

= Rs. 16

∴ Profit = 16 – 9

= Rs. 7

Profit % = Profit/C.P. × 100

= 7/9 × 100

= 700/9%

= 77 7/9%

**3. A man buys a certain number of articles at 15 for Rs. 112.50 and sells them at 12 for Rs.108. Find:**

**(i) his gain as percent;**

**(ii) the number of articles sold to make a profit of Rs.75.**

**Solution**

Let number of articles bought = 60

Note: L.C.M of articles bought = 60

Note: L.C.M. of 15 and 12 = 60

∴ C.P. of the articles = Rs. (112.50/15 × 60)

= Rs. (112.50 × 60)/15

= 112.50 × 4

= Rs. 450.00

And S.P. of the articles = Rs. 108/12 × 60

= Rs. 108 × 5

= Rs. 540

**(i)**Gain = S.P. – C.P.

= Rs. 540 – Rs 450

= Rs. 90

∴ Gain = Gain/C.P. × 100

= 90/450 × 100

= 100/5

= 20%

**(ii)**To make a profit of Rs. 90, the number of articles needed to be sold = 60

To make a profit of Re. 1 the number of articles needed to be sold = 60/90

To make a profit of Rs. 75, the number of articles needed to be sold = 60/90 × 75

= 4500/90

= 50

**4. A boy buys an old bicycle for Rs. 162 and spends Rs. 18 on its repairs before selling the bicycles for Rs. 207. Find his gain or loss percent.**

**Solution**

Buying price of the old bicycle = Rs. 162

Money spent on repairs = Rs. 18

Real C.P. of the bicycle = 162 + 18 = Rs. 180

S.P. of the bicycle = Rs 207

Profit = S.P. – C.P. = 207 – 162

= Rs. 45

Gain% = Profit/C.P. × 100

= 45/180 × 100

= 100/4

= 25%

**5. An article is bought from Jaipur for Rs. 4,800 and is sold in Delhi for Rs. 5,820. If Rs. 1,200 is spent on its transportations, etc. ; find he loss or the gain as percent.**

**Solution**

Cost price = Rs, 4,800

Selling Price = Rs 5,820

Transport etc. charges = Rs. 1,200

Total cost price = Rs. 4,800 + Rs. 1,200 = Rs.6,000

Loss = Rs. 6000 – Rs. 5820

= Rs. 180

∴ Loss % = 180/6000 × 100

= 3%

**6. Mohit sold a T.V. for Rs. 3,600; gaining one-sixth of its selling price. Find :**

**(i) the gain**

**(ii) the cost price of the T.V.**

**(iii) the gain percent.**

**Solution**

S.P. of T.V. = Rs. 3,600

Gain = 1/6 of (3600) = 1/6 × 3600

= Rs. 600

**(i)**Thus gain = Rs. 600

**(ii)**Cost Price = 3600 – 600

= Rs. 3000

**(iii)**Gain % = 600/3000 × 100

= 60/3

= 20%

**7. By selling a certain number of goods for Rs. 5,500; a shopkeeper loses equal to one-tenth of their selling price. Find :**

**(i) the loss incured**

**(ii) the cost price of the goods**

**(iii) the loss as percent.**

**Solution**

S.P. = Rs. 5,500

Loss = 1/10 of (S.P.) = 1/10 × 5500

= Rs. 550

**(i)**Loss incurred = Rs. 550

**(ii)**C.P. = Rs. 5,500 + Rs. 550

= Rs. 6,050

**(iii)**Loss% = (550 × 100)/6050

= (10 × 100)/110

= 100/11

= 9 1/11%

**8. The selling price of a sofa-set is times of its cost price. Find the gain or the loss as percent.**

**Solution**

Let the cost price (C.P.) = 1

S.P. = 1 × 4/5 = 4/5

∴ Loss = 1 – 4/5

= (5 – 4)/5

= 1/5

**[∵ Loss = C.P. – S.P.]**

∴ Loss% = Loss/C.P. = (1/5)/1 × 100

= 1/5 × 100

= 20%

**9. The cost price of an article is times of its selling price. Find the loss or the gain as percent.**

**Solution**

Let S.P. = 1

C.P. = 4/5 × 1 = 4/5

∴ Gain = S.P. – C.P.

**[∵ Gain = S.P. – C.P.]**

= 1 – 4/5

= (5 – 4)/5

= 1/5

∴ Gain % = Gain/C.P. × 100

= (1/5)/(4/5) × 100

= (1/5)/( 4/5) × 100

= 1/5 × 5/4 × 100

= 25%

**10. A shopkeeper sells his goods at 80% of their cost price. Find the percent gain or loses?**

**Solution**

Let C.P. of goods = Rs. 100

∴ S.P. of goods = 80/100 × 100

= Rs. 80

Loss = C.P. – S.P.

= Rs. 100 – Rs. 80

= Rs. 20

Loss% = Loss/C.P. × 100

= 20/100 × 100

= 20%

**11. The cost price of an article is 90% of its selling price. What is the profit or the loss as percent?**

**Solution**

Let S.P. of the article = Rs. 100

∴ C.P. of the article = 90/100 × 100

= Rs. 90

Gain = Rs. 100 – Rs. 90

= Rs. 10

Gain % = Gain/C.P. × 100

= 10/90 × 100

= 100/9 %

= 11 1/9%

**12. The cost price of an article is 30 percent less than its selling price. Find, the profit or loss as percent.**

**Solution**

Let S.P. of the article = Rs. 100

30% of S.P. = Rs. 30/100 × 100

= Rs. 30

∴ C.P. of the article = 100 – 30 = Rs. 70

Profit = S.P. – C.P.

Rs. 100 – Rs. 70

= Rs. 30

Profit% = Profit/C.P. × 100

= 30/70 × 100

= 300/7%

= 42 6/7%

**13. A shop-keeper bought 300 eggs at 80 paisa each. 30 eggs were broken in transaction and then he sold the remaining eggs at one rupee each. Find, his gain or loss as percent.**

**Solution**

C.P. of 300 egg@ 80 paise each = 300 × 80

= 24000 paise

= Rs. 240

No. of eggs which were broken in transaction = 30

Remaining eggs = 300 – 30

= 270

S.P. of eggs @ Rs. 1 each = 270 × 1

= Rs. 270

Gain = S.P. – C.P.

= Rs. 270 – Rs. 240

= Rs. 30

Gain % = Gain/C.P. × 100

= 30/240 × 100

= 100/8 %

= 12.5%

**14. A man sold his bicycle for Rs.405 losing one-tenth of its cost price, find :**

**(i) its cc price;**

**(ii) the loss percent.**

**Solution**

**(i)**Let C.P. of the bicycle = Rs. x

∴ Loss = Rs. x/10

S.P. = C.P. – Loss

= x – x/10

But, we are given S.P. = Rs. 405

∴ x – x/10 = 405

⇒ (10x – x)/10 = 405

⇒ 9x/10 = 405

⇒ x = 405 × 10/9

⇒ x = 4050/9

⇒ x = 4050/9

⇒ x = 450

∴ C.P. = Rs. 450

= 450/10

= Rs. 45

Loss % = Loss/C.P. × 100

= 45/450 × 100

= 4500/450 = 10 %

Gain = Rs. x/9

S.P. = Rs. (x + x/9) = Rs.(9x + x)/9 = Rs. 10x/9

But, we are given S.P. of the radio-set = Rs. 250

∴ 10x/9 = 250

⇒ x = 250 × 9/10

∴ C.P. = Rs. 450

**(ii)**Loss = x/10= 450/10

**...(Substituting the value of x)**= Rs. 45

Loss % = Loss/C.P. × 100

= 45/450 × 100

= 4500/450 = 10 %

**15. A man sold a radio-set for Rs.250 and gained one-ninth of its cost price. Find ;****(i) its cost price;****(ii) the profit percent.**

**Solution****(i)**Let C.P. of the radio-set = Rs. xGain = Rs. x/9

S.P. = Rs. (x + x/9) = Rs.(9x + x)/9 = Rs. 10x/9

But, we are given S.P. of the radio-set = Rs. 250

∴ 10x/9 = 250

⇒ x = 250 × 9/10

⇒ x = 25 × 9

⇒ x = 225

∴ C.P. of the radio set = Rs.225

= Rs. 225/9

= Rs. 25

Profit% = Profit/C.P. × 100

= 25/225 × 100

= (25 × 100)/225

= 100/9%

= 11 1/9%

∴ C.P. of the radio set = Rs.225

**(ii)**Profit = Rs. x/9= Rs. 225/9

**...(Substituting the value of x)**= Rs. 25

Profit% = Profit/C.P. × 100

= 25/225 × 100

= (25 × 100)/225

= 100/9%

= 11 1/9%

### Exercise 8 B

**1. Find the selling price, if:**

**(i) C.P. = Rs. 950 and profit = 8%**

**(ii) C.P. = Rs. 1,300 and loss = 13%**

**Solution**

**(i)**C.P. = Rs. 950 Profit = 8%

∴ S.P. = {950 × (100 + 8)}/100

= (950 × 108)/100

= 19 × 54

= Rs. 1026

**C.P. = Rs. 1,300**

(ii)

(ii)

Loss = 13%

∴ S.P. = {1300 × (100 – 13)}/100

= 13 × 87

= Rs. 1131

**2. Find the cost price, if :**

**(i) S.P. = Rs. 1,680 and profit = 12%**

**(ii) S.P. = Rs. 1,128 and loss = 6%**

**Solution**

**(i)**S.P. = Rs. 1, 128, Profit = 12%

C.P. = 100/(100 + profit) × S.P.

∴ C.P. = 100/(100 + 12) × 1680

= (100 × 1680)/112

= (25 × 1680)/28

= 25 × 60

= Rs. 1500

**(ii)**S.P. = Rs. 1,128, Loss = 6%

C.P. = 100/(100 – Loss) × S.P.

∴ C.P. = (100 × 1128)/(100 – 6)

= (100 × 1128)/94

= 100 × 12

= Rs. 1200

**3. By selling an article for Rs.900; a man gains 20%. Find his cost price and the gain.**

**Solution**

S.P. of an article = Rs. 900

Gain = 20%

C.P. = 100/(100 + Gain%) × S.P.

∴ C.P. = 100/(100 + 20) × Rs. 900

= Rs. 100/120 × 900

= Rs. 9000/12

= Rs. 750

Gain = S.P. – C.P.

= Rs. 900 – Rs. 750

= Rs. 150

**4. By selling an article for Rs.704; a person loses 12%. Find his cost price and the loss**

**Solution**

S.P. of an article = Rs. 704

Loss = 12%

C.P. = 100/(100 – Loss%) × S.P.

= 100/(100 – 12) × Rs. 704

= Rs. 100/88 × 704

= Rs. 100 × 8

= Rs. 800

Loss = C.P. – S.P.

= Rs. 800 – Rs. 704

= Rs. 96

**5. Find the selling price, if :**

**(i) C.P. = Rs.352; overheads = Rs.28 and profit = 20**

**(ii) C.P. = Rs.576; overheads = Rs.44 and loss = 16%**

**Solution**

**(i)**C.P. = Rs 352

Overheads = Rs. 28

Net C.P. = Rs. 352 + Rs. 28

= Rs. 380

Profit = 20%

We know = S.P. = (100 + Gain%)/100 × C.P.

= (100 + 20)/100 × 380 =

= Rs. 120/100 × 380

= 12 × 38

= Rs. 456

**(ii)**C.P. = Rs. 576

Overheads = Rs. 44

Net C.P. = Rs. 576 + Rs. 44

= Rs. 620

Loss = 16%

We know :

S.P. = (100 – Loss%)/100 × C.P.

= (100 – 16)/100 × Rs. 620

= Rs. 84/100 × 620

= Rs. 5208/10

= Rs. 520.80

**6. If John sells his bicycle for Rs. 637, he will suffer a loss of 9%. For how much should it be sold, if he desires a profit of 5 %?**

**Solution**

S.P. = Rs. 637, Loss = 9%

∴ C.P. = (100 × S.P.)/(100 – 9)

= 100/91 × 637

= 100 × 7

= Rs. 700

Profit = 5%

S.P. = (100 + Profit)/100 × C.P.

S.P. = (100 + 5)/100 × 700

= 105 × 7

= 735

**7. A man sells a radio-set for Rs.605 and gains 10%. At what price should he sell another radio of the same kind, in order to gain 16 %?**

**Solution**

In the first condition,

S.P. of a radio-set = Rs. 605

C.P. = 100/(100 + gain%) × S.P.

= 100/(100 + 10) × Rs. 605

= Rs. 100/110 × 605

= Rs. (100 × 605)/110

= 10 × 55

= Rs. 550

In the second condition:

C.P. = Rs. 550

Gain = 16%

S.P. = (100 + gain%)/100 × C.P.

= (100 + 16)/100 × Rs. 550

= Rs. 116/100 × 550

= Rs. (116 × 550)/100

= 58 × 111

= Rs. 638

∴ Radio should be sold at Rs. 638

**8. By selling a sofa-set for Rs.2,500; the shopkeeper loses 20%. Find his loss percent or profit percent; if he sells the same sofa-set for Rs.3150.**

**Solution**

In the first condition:

S.P. of a Sofa-set = Rs. 2500

Loss = 20%

∴ C.P. = 100/(100 – Loss%) × S.P.

= 100/(100 – 20) × Rs. 2500

= Rs. 100/80 × 2500

= Rs. (100 × 2500)/80

= (5 × 2500)/4

= 5 × 625

= Rs. 3125

In the second condition:

S.P. of the sofa-set = Rs. 3150

C.P. of the sofa-set = Rs. 3125

Gain = S.P. – C.P.

= Rs. 3150 – Rs. 3125

= Rs. 25

Gain% = Gain/C.P. × 100

= 25/3125 × 100

= (25 × 100)/3125

= 100/125

= 4/5%

= 0.8%

**9. Mr. Sinha sold two tape-recorders for Rs.990 each; gaining 10% on one and losing 10% on the other. Find his total loss or gain as percent on the whole transaction.**

**Solution**

In the case of first tape – recorder :

S.P. = Rs. 990

Gain = 10%

C.P. = 100/(100 + Gain%) × S.P.

= 100/(100 + 10) × Rs. 990

= Rs. 100/110 × 990

= Rs. 100 × 9

= Rs. 900

In the case of second tape-recorder :

S.P. = Rs. 990

Loss = 10%

C.P. = 100/(100 - Loss%) × S.P.

= 100(100 – 10) × Rs. 990

= 100/90 × 990

= 100 × 11

= Rs. 1100

Total C.P. of both the tape-recorders,

= Rs. 900 + Rs. 1100

= Rs. 2000

Total S.P. of both the tape-recorders = Rs 990 + Rs. 990

= Rs. 1980

Loss on the whole transaction = C.P. – S.P.

= Rs. 2000 – Rs. 1980

= Rs. 20

Loss% = Loss/C.P. × 100

= Rs. 20/Rs. 2000 × 100 – 2/2%

= 1%

**10. A tape-recorder is sold for Rs. 2,760 at a gain of 15% and a C.D. player is sold for Rs. 3,240 at a loss of 10% Find :**

**(i) the C.P. of the tape-recorder**

**(ii) the C.P. of the C.D. player.**

**(iii) the total C.P. of both.**

**(iv) the total S.P. of both**

**(v) the gain % or the loss % on the whole**

**Solution**

S.P. of tape-recorder = Rs, 2,760

Gain = 15%

**(i)**C.P. = (100 × S.P.)/115

**[C.P. = (100 × S.P.)/(100 + Gain)]**

= (100 × 2760)/115

= (20 × 2760)/23

= 20 × 120

= Rs. 2400

**(ii)**S.P. of C.D. player = Rs. 3,240

**[C.P. = 100/(100 – Loss) × S.P.]**

= 100/(100 – 10) × 3240

= 100/90 × 3240

= 100 × 36

= Rs. 3600

**(iii)**Total C.P. Of both = Rs. 2400 + Rs 3600 = Rs. 6000

**(iv)**Total S.P. of both = Rs. 2760 + Rs. 3240 = Rs. 6000

**(v)**Since, S.P. = C.P. there is no gain and no loss on the whole.

**11. Rajesh sold his scooter to Rahim at 8% loss and Rahim, in turn, sold the same scooter to Prem at 5% gain. If Prem paid Rs. 14,490 for the scooter ; find :**

**(i) the S.P. and the C.P. of the scooter for Rahim**

**(ii) the S.P. and the C.P. of the scooter for Rajesh**

**Solution**

Let C.P. of the scooter for Rajesh = Rs 100x

S.P. for Rajesh = (100x × 92)/100 = 92x

This will be C.P. for Rahim = 92x, Gain = 5%

∴ S.P. for Rahim = (92x × 105)/100

= (92x × 21)/20

= (46x × 21)/10

= 966x/10

This will be C.P. for Prem = Rs. 14,490

∴ 966x/10 = 14,490

⇒ x = 14490/966 × 10

= 14490/483 × 5

= 30 × 5

= 150

**(i)**C.P. of scooter for Rahim = 92x = 92 × 150

= Rs. 13800

S.P. of scooter for Rahim = 966x/10

= 966/10 × 150

= Rs. 966 × 15

= Rs. 14490

**(ii)**∴ C.P. of Scooter for Rajesh = 100x = 100 × 150

= Rs. 15000

S.P. of Scooter for Rajesh = 92x = Rs. 92 × 150

= Rs. 13800

**12. John sold an article to Peter at 20% profit and Peter sold it to Mohan at 5% loss. If Mohan paid Rs.912 for the article; find how much did John pay for it?**

**Solution**

Mohan paid for the article = Rs. 912

∵ Peter sold the article to Mohan

∴ For Peter :

S.P. = Rs. 912

Loss = 5%

C.P. = 100/(100 – Loss%) × S.P.

= 100/(100 – 5) × 912

= Rs. (100 × 912)/95

= 20 × 48

= Rs. 960

John sold the same article to Peter

∴ For John:

S.P. = Rs. 960

Profit = 20%

C.P. = 100/(100 + Profit%) × S.P.

= 100/(100 + 20) × Rs. 960

= Rs. 100/120 × 960

= Rs. 100 × 8

= Rs. 800

Hence, John paid for the article = Rs. 800

### Exercise 8 C

**1. A stationer buys pens at 5 for Rs.28 and sells them at a profit of 25 %. How much should a customer pay; if he buys**

**(i) only one pen ;**

**(ii) three pens?**

**Solution**

For Stationer:

C.P. of 5 pens = Rs. 28

C.P. of 1 pen = Rs.28/5 = Rs. 5.60

Profit = 25%

∴ S.P. of 1 pen = (100 + Profit%)/100 × C.P. of 1 Pen

= (100 + 25)/100 × Rs. 5.60

= Rs. 125/100 × 5.60

= Rs. (125 × 5.6)/100

= Rs. 5 × 1.4

= Rs 7

S.P. of 3 pens = 3 × 7 = Rs. 21

∴ Customer pays for

**(i)**only one pen = Rs. 7

**(ii)**Three pens = Rs. 21

**2. A fruit-seller sells 4 oranges for Rs. 3, gaining 50%. Find :**

**(i) C.P. of 4 oranges,**

**(ii) C.P. of one orange.**

**(iii) S.P. of one orange.**

**(iv) profit made by selling one orange.**

**(v) number of oranges brought and sold in order to gain Rs. 24.**

**Solution**

S.P. of 4 oranges = Rs. 3

∴ S.P. of 1 orange = Rs. ¾, Gain = 50%

S.P. = (C.P. × 150)/100

∴ C.P. of 1 orange = (100 × S.P.)/(100 + 50)

= (100 × ¾)/150

= 75/150

= Re ½

**(i)**C.P. of 4 oranges = 4 ×1/2 = Rs. 2

**(ii)**C.P. of 1 oranges = Rs. ½ = Rs. (0.50)

**(iii)**S.P. of 1 orange = Rs. ¾ = Rs. 0.75

**(iv)**Profit made by selling one orange = Rs. ¾ - Rs. ½

= Rs. ¼

= Rs. 0.25

**(v)**If gain is Rs. ¼; number of oranges = 1

If gain is Rs. 24, number of oranges = (1/1)/4 × 24

= 1 × 4/1 × 24

= 96

**3. A man sells 12 articles for Rs. 80 gaining 33%. Find the number of articles bought by the man for Rs. 90.**

**Solution**

S.P. of 12 articles = Rs. 80,

Gain = 33 1/3% = 100/3%

C.P. = 100/(100 + Gain) × S.P.

= 100/(100 + 100/3) × 80

= 100/{(300 + 100)/3} × 80

= 100/(400/3) × 80

= 100 × 3/400 × 80

= Rs. 60

Rs. 60 is the cost of 12 articles

Re. 1 is the cost of = 12/60 article

Rs. 90 is the cost of = 12/60 × 90

= 1/5 × 90 = 18

Man can buy article for Rs. 90 = 18

**4. The cost price of 20 articles is same as the selling price of 16 articles. Find the gain percent.**

**Solution**

C.P. of 20 articles = S.P. of 16 articles.

Let C.P. of 1 article = Re. 1

C.P. of 20 articles = Rs.20

and C.P. of 16 articles = Rs.16

S.P. of 16 articles = Rs.20

[S.P. of 16 articles = C.P. of 20 articles]

Gain = Rs.20 – Rs.16 = Rs.4

Gain% = 4/16 × 100

= (4/16 × 100)

= 25%

**5. The selling price of 15 articles is equal to the cost price of 12 articles. Find the gain or loss as percent.**

**Solution**

S.P. of 15 articles = C.P. of 12 articles

Let C.P. of 1 article = Re.1

C.P. of 12 article = Rs.12

and C.P. of 15 articles = Rs.15

S.P. of 15 articles = Rs.12

[S.P. of 15 articles = C.P. of 12 articles]

Loss = Rs.15 – Rs.12 = Rs.3

Loss% = 3/15 × 100 = 20%

**6. By selling 8 pens, Shyam loses equal to the cost price of 2 pens. Find his loss percent.**

**Solution**

Let C.P. of 1 pen = Re.1

C.P. of 2 pens = Rs.2

and C.P. of 8 pens = Rs.8

Loss = Rs.2 ..

**.[Loss = C.P. of 2 Pens]**

Loss% = 2/8 × 100 = 25%

**7. A shop-keeper bought rice worth Rs.4,500. He sold one-third of it at 10% profit.**

**If he desires a profit of 12% on the whole; find :**

**(i) the selling price of the rest of the rice ;**

**(ii) the percentage profit on the rest of the rice.**

**Solution**

C.P. of the rice = Rs. 4500

Profit desired on the whole = 12%

∴ S.P. of the whole rice = (100 + gain%)/100 × C.P.

= (100 + 12)/100 × Rs. 4500

= Rs. 112/100 × 4500

= 112 × 45

= Rs. 5040

C.P. of 1/3 of rice = 1/3 × Rs. 4500

= Rs. 1500

Since, gain on 1/3 of rice = 10%

∴ S.P. on it = (100 + gain%)/100 × C.P.

= (100 + 10)/100 × Rs. 1500

= Rs. 110/100 × 1500

= 11 × 150

= Rs. 1650

Remaining C.P. of the Rice = Rs. 4500 – Rs. 1500

= Rs. 3000

Remaining S.P. of the rice = Rs. 5040 – Rs. 1650

= Rs. 3390

Profit on the remaining rice = Rs. 3390 – Rs. 3000

= Rs. 390

Gain% on the remaining rice = 390/3000 × 100

= (390 × 100)/3000

= 13%

(i) ∴ S.P. of the rest of the Price = Rs. 3390

(ii) % Profit on the rest of the rice = 13%

**8. Mohan bought a certain number of note-books for Rs.600. He sold of them at 5 percent loss. At what price should he sell the remaining note-books so as to gain 10% on the whole?**

**Solution**

C.P. of note books = Rs. 600

Gain desired on the whole = 10%

∴ Total S.P. of all the note-books = (100 + gain%)/100 × C.P.

= (100 + 10)/100 × Rs. 600

= Rs. 110/100 × 600

= Rs. 660

C.P. of ¼ of the note-books = ¼ × Rs. 600

= Rs. 150

Loss on these note-books = 5%

∴ S.P. of these note-books = (100 – Loss%)/100 × C.P.

= (100 – 5)/100 × Rs. 150

= Rs. 95/100 × 150

= Rs. 14250/100

= Rs. 142.50

Now, C.P. of the remaining note-books = Rs. 600 – Rs. 150

= Rs. 450

Required S.P. of the remaining note-books = Rs. 660 – Rs. 142.50

= Rs. 517. 50

**9. Raju sells a watch at 5% profit. Had he sold it for Rs.24 more; he would have gained 11%. Find the cost price of the watch.**

**Solution**

Let C.P. of the watch = Rs.100

When profit = 5%;

S.P. = Rs.(100 + 5) = Rs.105

When profit = 11%;

S.P. = Rs.(100 + 11) = Rs .111

Difference of two selling prices = Rs. 111 – Rs. 105 = Rs.6

When watch sold for Rs.6 more; then C.P. of the watch = Rs.100

When watch sold for Re. 1 more; then C.P. of the watch = Rs. 100/6

When watch sold for Rs.24 more; then C.P. of the watch = Rs. 100/6 × 24 = Rs.400

**Question 10: A man sold a bicycle at 5% profit. If the cost had been 30% less and the selling price Rs.63 less, he would have made a profit of 30%. What is the cost price of the bicycle?**

**Solution 10:**

Let C.P. of the bicycle = Rs.100

In the I case :

When Profit = 5% ;

S.P. = Rs. (100 + 5) = Rs. 105

In the II case:

C.P. = (100 – 30/100 × 100)

= Rs. (100 – 30)

= Rs. 70

Profit = 30%

S.P. = (100 + Profit)/100 × C.P.

= (100 + 30)/100 × Rs. 70

= 130/100 × Rs. 70

= Rs. (130 × 70)/100

= Rs. 91

Difference of two selling prices = Rs. 105 – Rs. 91

= Rs. 14

If difference is Rs. 14 then C.P. of the bicycle = Rs. 100

If difference is Re. 1 then C.P. of the bicycle = Rs. 100/14

If difference is Rs. 63 then C.P. of the bicycle = Rs. 100/14 × 63

= Rs. (100 × 63)/14

= Rs. 50 × 9

= Rs. 450

**11. Renu sold an article at a loss of 8 percent. Had she bought it at 10% less and sold for Rs.36 more; she would have gained 20%. Find the cost price of the article.**

**Solution**

Let C.P. of the article = Rs. 100

In the I case : When loss = 8%

S.P. = Rs. (100 – 8)

= Rs. 92

In the II case: C.P. = Rs. (100 – 10/100 × 100)

= Rs. (100 – 10)

= Rs. 90

Profit = 20%

S.P. = (100 + 20)/100 × C.P.

= 120/100 × Rs. 90

= Rs. 12 × 9

= Rs. 108

Difference of two selling prices = Rs. 108 – Rs. 92

= Rs. 16

If the difference of two selling prices is Rs. 16 then C.P. = Rs 100

If the difference of two selling prices is Re. 1 then C.P. = Rs 100/16

If the difference of two selling prices is Rs. 36 then C.P. = Rs 100/16 × 36

= Rs. (100 × 36)/16

= Rs. 25 × 9

= Rs. 225

### Exercise 8 D

**1. An article is marked for Rs. 1,300 and is sold for Rs. 1,144; find the discount percent.**

**Solutions**

Marked price = Rs. 1,300 , S.P. = Rs. 1,144

Discount = Rs. 1,300 – Rs. 1,114

= Rs. 156

∴ Discount % = 156/1300 × 100

= 156/13

= 12%

**2. The marked price of a dinning table is Rs. 23,600 and is available at a discount of 8%. Find its selling price.**

**Solution**

Marked Price = Rs. 23,600, Discount = 8%

∴ S.P. = 23,600 × (100 – 8)/100

= 236 × 92

= Rs. 21, 712

**3. A wrist-watch is available at a discount of 9%. If the list-price of the watch is Rs. 1,400; find the discount given and the selling price of the watch.**

**Solution**

List price of the watch = Rs. 1,400

Discount = 9%

Discount = (1400 x 9)/100 = 14 x 9 = Rs. 126

S.P. = (List price – Discount) = Rs. (1400 – 126) = Rs. 1274

**4. A shopkeeper sells an article for Rs. 248.50 after allowing a discount of 10%. Find the list price of the article.**

**Solution**

S.P. of the article = Rs. 248.50

Discount = 10%

Let M.P. = Rs. 100

Discount = 10/100 × Rs. 100

= Rs. 10

Selling Price = Rs. 100 – Rs. 10

= Rs. 90

If S.P. is Rs. 90; then M.P. = Rs.100

If S.P. is Re 1; then M.P. = Rs.100/90

If S.P. is Rs. 248.50; then M.P. = Rs.100/90 × 248.50

= Rs. (100 × 248.50)/90

= Rs. 24850/90

= Rs. 276.11

**(Approx.)**

**5. A shop-keeper buys an article for Rs.450. He marks it at 20% above the cost price. Find :**

**(i) the marked price of the article.**

**(ii) the selling price, if he sells the articles at 10 percent discount.**

**(iii) the percentage discount given by him, if he sells the article for Rs.496.80**

**Solution**

C.P. of the article = Rs. 450

**(i)**Marked price of the article = (100 + 20)/100 × Rs. 450

= Rs. 120/100 × 450

= 12 × 45

= Rs. 540

**(ii)**Discount = 10/100 × M.P.

= 10/100 × Rs. 540

= Rs. 54

S.P. = M.P. – Discount

= Rs. 540 – Rs. 54

Rs. 486

**(iii)**S.P. = Rs. 496.80

M.P. = Rs. 540

Discount = M.P. – S.P.

= Rs. 540 – Rs. 496.80

= Rs. 43.20

Discount % = Discount/M.P. × 100

= 43.20/540 × 100

= 4320/540 %

= 8%

**6. The list price of an article is Rs.800 and is available at a discount of 15 percent. Find :**

**(i) selling price of the article ;**

**(ii) cost price of the article, if a profit of 13 % is made on selling it.**

**Solution**

List price of

**the article = Rs. 800**

Discount @ 15% = 15/100 × Rs. 800

**(i)**S.P. of the article = RS. 800 – Rs. 120

= Rs. 680

**(ii)**S.P. of the article = Rs. 680

Profit = 13 1/3%

= 40/3 %

C.P. = 100/(100 + Profit %) × S.P.

= 100/(100 + 40/3) × Rs. 680

= 100/340/3 × Rs. 680

= 3/340 × 100 × 680

= 3 × 100 × Rs. 2

= Rs. 600

**7. An article is marked at Rs. 2,250. By selling it at a discount of 12%, the dealer makes a profit of 10%. Find :**

**(i) the selling price of the article.**

**(ii) the cost price of the article for the dealer.**

**Solution**

**(i)**Market Price = Rs. 2,250

S.P. = {2250(100 – 12)}/100

= (2250 × 88)/100

= 45 × 44

= Rs. 1980

**(ii)**S.P. = Rs. 1980, Profit = 10%

∴ C.P. of the article = 100/110 × 1980

= 100 × 18

= Rs. 1800

**8. By selling an article at 20% discount, a shopkeeper gains 25%. If the selling price of the article is Rs. 1,440; find :**

**(i) the marked price of the article.**

**(ii) the cost price of the article.**

**Solution**

S.P. of the article = Rs. 1440

Let marked Price = Rs. 100x

Discount = 20%

∴ S.P. = {100x(100 – 20)/100}

= 80x

According to statement, 80x = 1440

x = 1440/80 ⇒ x =18

∴ x = 18

∴ Marked price = 100x = 100 × 18

= Rs. 1800

S.P. = Rs. 1440

Profit = 25%

∴ C.P. = (100 × S.P.)/(100 + 25)

= (100 × 1440)/125

= 4/5 × 1440

= 4 × 288

= Rs. 1152

**9. A shop-keeper marks his goods at 30 percent above the cost price and then gives a discount of 10 percent. Find his gain percent.**

**Solution**

Let C.P. of the goods = Rs. 100

M.P. of the goods = Rs 100 + Rs. 30

= Rs. 130

Discount = 10/100 × Rs. 130

= Rs. 1300/100

= Rs. 13

S.P. of the goods = M.P. – Discount

= Rs 130 – Rs. 13

= Rs. 117

Gain = S.P. – C.P.

= Rs. 117 – Rs. 100

= Rs. 17

Gain% = Gain/C.P. × 100

= 17/100 × 100

= 177%

**10. A ready-made garments shop in Delhi, allows 20 percent discount on its garments and still makes a profit of 20 percent. Find the marked price of a dress which is bought by the shop-keeper for Rs.400.**

**Solution**

C.P. of the dress = Rs. 400

Profit = 20/100 × Rs. 400

= Rs. 80

S.P. = C.P. + Profit

= Rs. 400 + Rs. 80

= Rs. 480

Let, M.P. of the dress = Rs. 100

Discount @ 20% = 20/100 × Rs. 100

= Rs. 20

S.P. of the dress = M.P. – Discount

= Rs. 100 – Rs. 20

= Rs. 80

If S.P. of the dress is ₹ 80; then M.P. = ₹ 100

If S.P. of the dress is ₹ 1 then M.P. = ₹ 100/80

If S.P. of the dress is ₹ 480 then M.P. = ₹ 100/80 × 480

= ₹ 100 × 6 = 600

∴ M.P. of the dress = ₹ 600

**11. At 12% discount, the selling price of a pen is Rs. 13.20. Find its marked price. Also, find the new selling price of the pen, if it is sold at 5% discount.**

**Solution**

Let marked price = ₹100x

Discount = 12%

∴ S.P. = {100x(100 – 12)}/100

= (100x × 88)/100

= 88x

According to statement,

88x = 13.20

∴ x = 13.20/88 = 1320/(88 × 100)

= 30/200

= 3/20

∴ Marked price 100x = (100 × 3)/ 20

= ₹ 15

New S.P. = (15 × 95)/20

**[∵ discount = 5%]**

= (15 × 19)/20

= (3 × 19)/4

= 57/4

= ₹ 14.25

**12. The cost price of an article is Rs. 2,400 and it is marked at 25% above the cost price. Find the profit and the profit percent, if the article is sold at 15% discount.**

**Solution**

C.P. = ₹ 2, 400

∴ Marked Price = 2400(100 + 25)/100

= 24 × 125

= ₹ 3000

Discount = 15%

∴ S.P. = 3000 × (100 – 15)/100 = 30 × 85 = ₹ 2550

∴ Profit = ₹2550 – ₹ 2400

= ₹ 150

Profit% = 150/2400 × 100

= 50/8

= 25/4

= 6 ¼%

**13. Thirty articles are bought at Rs. 450 each. If one-third of these articles be sold at 6% loss; at what price must each of the remaining articles be sold in order to make a profit of 10% on the whole?**

**Solution**

C.P of one article = ₹ 450

C.P. of 30 articles = ₹ 450 × 30

= ₹ 13500

C.P. of 1/3 articles = ₹ 450 × 30/3

= ₹ 4500

Loss of = 6%

∴ S.P. of 10 articles = C.P. × (100 – Loss%)/100

= ₹{4500 × (100 – 6)}/100

= ₹(4500 × 94)/100

= ₹ 4230

C.P. of remaining articles = ₹ 4500 × 20

= ₹9000

Profit on the whole = 10%

∴ Total S.P. of 30 articles = ₹(13500 × (100 + 10)/100

= ₹(13500 × 110)/100

= ₹14850

∴ S.P. of remaining 20 articles = ₹14850 - ₹ 10620

∴ S.P. of 1 article = ₹10620/20

= ₹531

**14. The cost price of an article is 25% below the marked price. If the article is available at 15% discount and its cost price is Rs. 2,400; find:**

**(i) Its marked price**

**(ii) its selling price**

**(iii) the profit percent.**

**Solution**

Let M.P. of an article = ₹100

∴ Cost Price = 100 × (100 – 25)/100

= ₹ (100 × 75)/100

= ₹ 75

Discount = 15%

∴ S.P. = ₹ 100 - ₹ 15 = ₹ 85

But cost price = ₹2400

**(i)**∴ Marked price = ₹2400 × 100/75

= ₹32 × 100

= ₹3200

**(ii)**and S.P. = ₹(3200 × 85)/100

= ₹2720

**(iii)**Profit = S.P. – C.P.

= ₹ 2720 – 2400

= ₹ 320

∴ Profit % = (Profit × 100)/C.P.

= (320 × 100)/2400

= 40/3%

= 13 1/3%

**15. Find a single discount (as percent) equivalent to following successive discounts:**

**(i) 20% and 12%**

**(ii) 10%, 20% and 20%**

**(iii) 20%, 10% and 5%**

**Solution**

**(i)**Successive discount = 20% and 12%

Let M.P. = ₹ 100

First discount = 20%

Second discount = 12%

∴ S.P. = M.P.(100 – Discount%)/100

= {100 × (100 – 20)(100 – 12)/(100 × 100)

= (100 × 80 × 88)/(100 × 100)

= 352/5

∴ Total discount on ₹ 100 = 100 – 352/5

= (500 – 352)/5

= ₹148/5

∴ Single discount = 148/5%

= 29 3/5%

**(ii)**Successive discounts 10%, 20% and 20%

Let M.P. = ₹100

∴ S.P. after 3 discounts = {100(100 – 10)(100 – 20)(100 – 20)}/(100 × 100 × 100)

= (100 × 90 × 80 × 80)/(100 × 100 × 100)

= 576/10

∴ Total discount = ₹100 – 576/10

= ₹(1000 – 576)/10

= 424/10

∴ Single discount = 424/10% = 42.4%

**(iii)**Successive discounts = 20%, 10%, 5%

Let M.P. = ₹ 100

∴ S.P. after three discounts = ₹{100(100 – 20)(100 – 10)(100 – 5)/(100 × 100 × 100)

= ₹(100 × 80 × 90 × 95)/(100 × 100 × 100)

= ₹342/5

∴ Total discount = 100 - 342/5

= (500 – 352)/5

= 158/5

∴ Single discount = 158/5 % = 31.6%

**16. Find the single discount (as percent) equivalent to successive discounts of:**

**(i) 80% and 80%**

**(ii) 60% and 60%**

**(iii) 60% and 80%**

**Solution**

**(i)**Successive discounts = 80% and 80%

Let M.P. = ₹100

Then S.P. after two discounts = ₹{100 (100 – 80)(100 – 80)/(100 × 100)

= (100 × 20 × 20)/(100 × 100)

= ₹4

∴ Total discounts = ₹ 100 – 4 = ₹96

∴ Single discount = 96%

**(ii)**Successive discounts = 60% and 60%

Let M.P. = ₹100

Then S.P. after two discounts, = {100(100 – 60)(100 – 60)/(100 × 100)

= (100 × 40 × 40)/(100 × 100)

= ₹16

∴ Total discount = ₹ 100 – 16 = ₹84

Single discount = 84 %

**(iii)**Successive discounts = 60% and 80%

let M.P. = ₹ 100

∴ S.P. after two discounts = ₹{100(100 - 60)(100 - 80)/(100 × 100)

= ₹(100 × 40 × 20)/(100 × 100)

= ₹ 8

∴ Total discount = ₹ 100 – 8 = ₹92

∴ Single discount = 92%

### Exercise 8 E

**1. Rajat purchases a wrist-watch costing Rs. 540. The rate of Sales Tax is 8%. Find the total amount paid by Rajat for the watch.**

**Solution**

Cost of watch = ₹540

Rate of Sales Tax = 8%

∴ Amount of Sales Tax = ₹540 × 8/100

= ₹4320/100

= ₹43.20

Total Amount of Watch = ₹540 + ₹43.20

= ₹ 583.20

**2. Ramesh paid ₹ 345.60 as Sales Tax on a purchase of ₹ 3,840. Find the rate of Sales Tax.**

**Solution**

On ₹3840, sales-tax is = ₹345.60

∴ Percent of Sales Tax = (345.60 × 100)/3840

= (34560 × 100)/(100 × 3840)

= 9%

**3. The price of a washing machine, inclusive of sales tax is ₹ 13,530/-. If the Sales Tax is 10%, find its basic (cost) price.**

**Solution**

Selling price of Washing machine = ₹13,530

Rate of Sales Tax = 10%

∴ Cost Price = (Selling Price × 100)/(100 + Rate of Sales Tax)

= (13530 × 100)/(100 + 10)

= (13530 × 100)/110

= ₹12,300

**4. Sarita purchases biscuits costing ₹ 158 on which the rate of Sales Tax is 6%. She also purchases some cosmetic goods costing ₹ 354 on which rate of Sales Tax is 9%. Find the total amount to be paid by Sarita.**

**Solution**

Cost of biscuits = ₹158

Sales Tax @ 6% = ₹158 × 6/100

= 948/100

= ₹9.48

Total price of biscuits = ₹158 + ₹9.48

= ₹167.48

Cost of cosmetic-goods = ₹354

Sales Tax @9% = ₹354 × 9/100

= 3186/100

= ₹31.86

Total Cost of cosmetic goods = ₹354 + ₹31.86 = ₹385.86

Total amount paid by Sarita = 167.48 + 385.86 = ₹535.34

**5. The price of a T.V. set inclusive of sales tax of 9% is ₹ 13,407. Find its marked price. If Sales Tax is increased to 13%, how much more does the customer has to pay for the T.V.?**

**Solution**

Sale price of T.V. set = ₹13,407

Rate of sales ttax = 9%

Let marked price of T.V. = x

Then sale price = x + (x × 9)/100

= (100x + 9x)/100

= 109x/100

∴ 109x/100 = ₹ 13,407

x = (13407 × 100)/109

= ₹ 12,300

∴ Marked Price = ₹12,300

In second case, Sales Tax = 13%

∴ Amount of sales Tax = ₹12,300 × 13/100

= ₹1,599

∴ Sale price = ₹12,300 + 1,599 = ₹ 13,899

Difference between the two sales price = ₹13,899 - ₹ 13,407

= ₹ 492

**6. The price of an article is ₹ 8,250 which includes Sales Tax at 10%. Find how much more or less does a customer pay for the article, if the Sales Tax on the article:**

**(i) increases to 15%**

**(ii) decreases to 6%**

**(iii) increases by 2%**

**(iv) decreases by 3%**

**Solution**

Price of an article = ₹ 8,250

Rate of Sales Tax = 10%

Let the list price = x

∴ Sales tax = x × 10/100 = x/10

Sales price = x + x/10 = 11x/10

∴ 11x/10 = 8250

x = (8250 × 10)/11 = 7,500

∴ List price = ₹7,500

**(i)**Rate of sales tax = 15%

∴ Sale Price = ₹ 7,500 (100 + 15)100

= ₹7,500 × 115/100

= ₹ 8,625

∴ Customer will pay more.

Hence increase = 8,625 – 8,250 = ₹375

∴ Sale Price = ₹7,500 × (100 + 12)/100

= ₹ 7,500 × 107/100 = ₹ 8,025

∴ The customer will have to pay less = ₹8,250 - ₹ 8,025

= ₹ 225

**7. A bicycle is available for ₹ 1,664 including Sales Tax. If the list price of the bicycle is ₹ 1,600, find :**

**(i) the rate of Sales Tax**

**(ii) the price a customer will pay for the bicycle if the Sales Tax is increased by 6%.**

**Solution**

**8. When the rate of sale-tax is decreased from 9% to 6% for a coloured T.V.; Mrs Geeta will save ₹ 780 in buying this T.V. Find the list price of the T.V.**

**Solution**

Rate of sales tax in the beginning = 9%

And Reduced rate = 6%

∴ Diff. = 9 – 6 = 3%

Total saving = ₹ 780

∴ List price of TV = Total saving × 100/3

= (780 × 100)/3

= ₹26000

**9. A shopkeeper sells an article for ₹ 21,384 including 10% sales-tax. However, the actual rate of sales-tax is 8%. Find the extra profit made by the dealer.**

**Solution**

Sale Price of an article including S.T. = ₹ 21384

Rate of Sales Tax = 10%

∴ Actual price = (Total price × 100)/(100 + ST%)

= (21384 × 100)/(100 + 10)

= (21384 × 100)/110

= ₹ 19440

In the second case, rate of sales tax = 8%

∴ S.P. = ₹{19440 ×(100 + 8)/100}

= ₹(19440 × 108)/100

= ₹ 2099520/100

= ₹20995.20

∴ Extra profit = ₹21384 - ₹ 20995.20

= ₹388.80

### Exercise 8 F

**1. A shopkeeper buys an article for ₹ 8,000 and sells it for ₹ 10,000. If the rate of tax under VAT is 10%, find :**

**(i) tax paid by the shopkeeper**

**(ii) tax charged by the shopkeeper**

**(iii) VAT paid by the shopkeeper**

**Solution**

Cost Price of an article = ₹8000

And, selling price = ₹10,000

**(i)**Tax paid by Shopkeeper under VAT 10% = ₹(8,000 × 10)/100

= ₹800

**(ii)**Tax charged by the shopkeeper

∵ Selling price = ₹10,000 under VAT 10%

= ₹(10,000 × 10)/100

= ₹1000

**VAT paid by the shopkeeper = ₹1000 - ₹800 = ₹200**

(iii)

(iii)

**2. A trader buys some goods for ₹ 12,000 and sells them for ₹ 15,000. If the rate of tax under VAT is 12%, find the VAT paid by the trader?**

**Solution**

Cost price of goods = ₹12,000

VAT charged, under VAT 12% = (12,000 × 12)/100

= ₹1440

Selling price of goods = ₹15,000

VAT charged, Under VAT 12% = (15,000 × 12)/100

= ₹1800

VAT paid by trader = ₹1800 - ₹1400

= ₹360

**3. The marked price of an article is ₹ 7,000 and is available at 20% discount. Manoj buys this article and then sold it at its marked price. If the rate of tax at each state is 10%, find the VAT paid by Manoj.**

**Solution**

M.P. of an article = ₹7000

Discount rate = 20%

C.P. for Manoj = ₹7000 – 20% of ₹7000

= ₹7000 - ₹1400

= ₹5600

∴ Tax paid for Manoj = ₹(5600 × 10)/100

= ₹560

S.P. of an article = ₹7000

Tax charged by Manoj = ₹(7000 × 10)/100

= ₹700

VAT paid = Tax charged – Tax paid

= ₹700 - ₹560

= ₹140

**4. A buys some goods for ₹ 4,000 and sold them to B for ₹ 5,000. B sold these goods to C for ₹ 6,000. If the rate of tax (under VAT) at each stage is 5%, find :**

**(i) VAT paid by A**

**(ii) VAT paid by B**

**Solution**

C.P. of some goods for A = ₹ 4000

C.P. of some goods for B = ₹ 5000

and C.P. for C = ₹ 6000

Rate of VAT in each case = 5%

∴ VAT charged by A = ₹4000 × 5/100 = ₹200

VAT charged by B = ₹5,000 × 5/100 = ₹250

VAT charged by C = ₹6000 × 5/100 = ₹300

(i) Now VAT paid by A = ₹250 - ₹200 = ₹50

(ii) Now VAT paid by B = ₹300 - ₹250 = ₹50

**5.A buys an article for ₹ 8,000 and sold it to B at 20% profit. If the rate of tax under VAT is 8%, find :**

**(i) tax paid by A**

**(ii) tax charged by A**

**(iii) VAT paid by A**

**Solution**

**6. A shopkeeper purchases an article for ₹ 12,400 and sells it to a customer for ₹ 17,000. If the tax under VAT is 8%, find the VAT paid by the shopkeeper.**

**Solution**

C.P. of article = ₹ 12,400

Rate of VAT = 8%

Total VAT = ₹ 12,400 × 8/100 = ₹ 992

S.P. of the article = ₹ 17000

VAT charge 8% = ₹ 17000 × 8/100 = ₹ 1360

Amount of VAT paid by the shopkeeper = ₹ 1360 – ₹ 992 = ₹ 368

**7. A purchases an article for ₹ 7,200 and sells it to B for ₹ 9,600. B, in turn, sells the article to C for ₹ 11,000. If the tax (under VAT) is 10%, find the VAT paid by A and B.**

**Solution**

C.P. of an article for A = ₹ 7,200

C.P. of the article for B = ₹9600

And C.P. for C = ₹11000

Rate of VAT in each case = 10%

∴ VAT charged by A = ₹7200 × 10/100 = ₹ 720

VAT charged by B = ₹9600 × 10/100 = ₹960

And VAT charged by C = ₹11000 × 10/100

= ₹1100

Now VAT levied on A = ₹960 - ₹720

= ₹240

And VAT levied on B = ₹1100 - ₹960

= ₹140

**8. A manufacturer buys some goods for ₹ 60,000 and pays 5% tax. He sells these goods for ₹ 80,000 and charges tax at the rate of 12%. Find the VAT paid by the manufacturer.**

**Solution**

C.P. of raw material = ₹60000

Rate of tax = 5%

∴ Total tax = ₹60000 × 5/100 = ₹3000

S.P. of that material = ₹80,000

Rate of tax = 12%

∴ Total tax = ₹80,000 × 12/100 = ₹ 9600

VAT paid by manufacturer = ₹ 9600 - ₹3000 = 6600

**9. The cost of an article is ₹ 6,000 to a distributor, he sells it to a trader for ₹ 7,500 and the trader sells it further to a customer for ₹ 8,000. If the rate of tax under VAT is 8%; find the VAT paid by the:**

**(i) distributor**

**(ii) trader**

**Solution**

Cost price of an article to a distributor = ₹6000

And selling price of distributor = ₹7500

And selling price of trader = ₹8000

Rate of VAT = 12.5% = 25/2%

Now, VAT for two distributor = ₹(6000 × 25)/(100 × 2)

= ₹750

And VAT for two trader = (7500 × 25)/(100 × 2)

= ₹937.50

And VAP for customer = (8000 × 25)/(100 × 2)

= ₹1000

(i) Now VAT paid by distributor = ₹937.50 - ₹750

= ₹ 187.50

(ii) and VAT paid by trader = ₹1000 - ₹937.50 = ₹62.50

**10. The marked price of an article is ₹ 10,000. A buys it at 30% discount on the marked price and sells it at 10% discount on the marked price. If the rate of tax under VAT is 5%, find the amount of VAT paid by A.**

**Solution**

M.P. of an article = ₹10,000

A purchased it at discount of = 30%

C.P. of an article = M.P. – (Discount rate × M.P.)/100

= ₹10,000 – (30 × 10,000)/100

= ₹10,000 - ₹3000

= ₹7000

Tax rate = 5%

Tax paid by A = C.P. × Tax rate/100

= ₹7000 × 5/100

= ₹350

Now, A sold the article at 10% discount

∴ S.P. of an article = M.P. – (Discount rate × M.P.)/100

= ₹10,000 – (10 × ₹10,000)/100

= ₹10,000 - ₹1000 = ₹9000

Tax charged by A = S.P. × Tax rate/100

= ₹9000 × 5/100 = ₹450

∴ VAT paid by A = Tax charged – Tax paid

= ₹450 - ₹ 350

= ₹100