# ICSE Solutions for Chapter 1 Value Added Tax Class 10 Mathematics

Question 1: Rajat purchases a wrist watch costing  ₹ 540. The rate of sales tax is 8%. Find the total amount paid by Rajat for the watch

Solution 1: Sale price of watch = ₹ 540
Rate of sales tax = 8%
Total amount paid by Rajat = ₹540 + 8% of ₹540
=  ₹540 + 8/100 × 540
= ₹540 + ₹ 43.20
= ₹583.20

Question 2 Ramesh paid ₹ 345.60 as sales tax on a purchase of ₹ 3,840. Find the rate of sales tax.

Solution 2: Sale price = ₹3,840
Sales tax paid = ₹345.60
∴ Rate of sales tax = (sales tax/sale price) × 100%
= (345.60/3,840)× 100%
= 9%

Question 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 3: Selling price of washing machine = ₹ 13,530
Rate of sales tax = 7%
Selling price× 100
∴ Cost price = (Selling price × 100/100 + Rate of sales tax)
= (13530 × 100/100 +10)
= 1353000/110
= Rs. 12300

Question 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 the rate of sales tax is 9%. Find the total amount to be paid by Sarita.

Solution 4: Sale price of biscuits = ₹ 158
Rate of sales tax on biscuits = 6%
Amount paid for biscuits = ₹ 158 + 6% of  ₹ 158
= ₹ 158 + 6/100 × 158
= ₹ 158 + ₹ 9.48
= ₹ 167.48
Sale price of cosmetic goods = ₹ 354
Rate of sales tax = 9%
Amount paid for cosmetic goods = ₹ 354 + 9% of ₹ 354
= ₹ 354 + 9/100 ×354
= ₹ 354 + ₹ 31.86
= ₹ 385.86
Total amount paid by Sarita = ₹ 167.48 + ₹ 385.86
= ₹ 553.34

Question 5. The marked price of two articles A and B together is ₹ 6,000. The sales tax on article A is 8% and that on article B is 10%. If on selling both the articles, the total sales tax collected is ₹ 552, find the marked price of collected of the articles A and B.

Solution 5: Let the marked price of article A be ₹ x and article B be ₹ y.
The marked price of A and B together is ₹ 6,000.
⇒ x + y = 6,000 .... (i)
The sales tax on article A is 8% and that on article B is 10%
Also the total sales tax collected on selling both the articles is ₹ 552.
⇒  8% of x + 10% of y = 552
⇒ 8x + 10y = 55,200 ...(ii)
Multiply equation (i) by 8 and subtract it from equation (ii) we get,
2y = 7,200
⇒ y = 3,600
Substituting y = 3,600 in equation (i) we get,
x + 3,600 =  6,000
⇒ x = 2,400
The marked price of article A is ₹ 2.400 and article B is ₹ 3.600.

Question 6: The price of a TV 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 6:
Total price paid for T.V. = ₹ 13,407
Rate of sales tax = 9%
Let sale price = ₹ y
According to question,
y + 9% of y = Rs 13,407
⇒ y + 9y/100 = Rs 13,407
= 109y/100 = Rs 13,407
⇒ y = (13,407 × 100)/100
= Rs12,300
New rate of sales tax = 13%
New total price for T.V. = ₹ 12,300 + 13% of ₹ 12,300
= ₹ 12,300 + 13/100 x 12,300
= 12,300 + ₹ 1,599
= ₹ 13,899
More money paid = ₹13,899 - ₹13,407 = ₹ 492

Question 7. 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 7: Let sale price of article = ₹ y
Total price inclusive of sales tax = ₹ 8,250
Rate of sales tax = 10%
According to question
y + 10% of y = Rs 8,250
⇒  y + y/10 = Rs 8,250
⇒ 11y/10  = Rs 8,250
⇒ y = (8,250 × 10)/11
=  Rs7,500

(i) New rate of sales tax = 15%
New total price = ₹ 7,500 + 15% of ₹ 7,500
= ₹ 7,500 + 15/100 × 7,500
= ₹7,500 +  ₹ 1,125 = ₹ 8,625
More money paid = ₹ 8,625 - ₹ 8,250 = ₹ 375

(ii) New rate of sales tax = 6%
New total price = ₹7,500 + 6% of ₹ 7,500
= ₹ 7,500 + 6/100 × 7,500
= ₹ 7,500 + ₹ 450 = ₹ 7,950
Less money paid = ₹ 8,250 - ₹ 7950 = ₹ 300

(iii) New rate of sale tax = (10 + 2)%  = 12%
New total price = ₹ 7,500 + 12% of ₹ 7,500
= ₹  7500 + 12/100 × 7500
= ₹ 7,500 + ₹ 900 = ₹ 8,400
More money paid = ₹ 8,400 - ₹ 8,250 = ₹ 150

(iv) New rate of sales tax = (10 – 3) % = 7%
New total price = ₹ 7,500 + 7% of ₹ 7500
= ₹ 7500 + 7/100 × 7,500
= ₹ 7,500 + ₹ 525 = ₹ 8,025
Less money paid = ₹ 8,250 - ₹ 8,025  = ₹ 225

Question 8: 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 pray for the bicycle if the sales tax is increased by 6%

Solution 8:
Price of bicycle inclusive of sales tax = ₹ 1,664
List price of bicycle = ₹ 1,600

(i) Sales tax = ₹ 1,664 - ₹ 1600 = ₹ 64
∴ Rate of sales tax = sales tax/list price × 100% = 64/1,600 × 100% = 4%

(ii) New rate of sales tax = (4 + 6)% = 10%
New total price = ₹ 1,600 + 10% of ₹ 1,600
= ₹ 1,600 + 10/100 × 1,600
= ₹ 1600 + ₹ 160
= ₹ 1,760

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

Solution 9: Let the list price of TV.= y
Sales tax when the rate is 9% = 9/100 y
⇒  Sale price is y + 9y/100
Sales tax when the rate is 6% = 6/100y
⇒  Sale price is y + 6/100y
Differences of sale prices
=  y + 9y/100 – (y + 6y/100)
= y + 9y/100 – y – 6y/100
= 9y/100 – 6y/100
Savings for Geeta = 784.

Therefore, we have,
784  = 9y/100 – 6y/100
⇒  3y/100  = 78
⇒ y = (78 ×100)/3
⇒  y = Rs. 26,000
Thus the list price of the T.V. is Rs.26,000

Question 10. A trader buys an unfinished article for ₹ 1,800 and spends 600 on its finishing, packing, transportation, etc. He marks the article at such a price that will give him 20% profit. How much will a customer pay for the article including 12% sales tax.

Solution 10: Purchase price = ₹ 1,800
Expenditure = ₹ 600
Total price = ₹ 1,800 + ₹ 600 = ₹ 2,400
M.P of article = ₹ 2,400 + 20% of  ₹ 2400
= ₹ 2,400 + 20/100 × 2400
= ₹ 2,400 + ₹ 480 = ₹ 2,880
Cost price for customer = ₹ 2,880 + 12% of ₹ 2,880
= ₹ 2,880 + 12/100 x 2880
= ₹ 2,880 + ₹ 345.60
= ₹ 3,225.60