# 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

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

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

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

Price of bicycle inclusive of sales tax = ₹ 1,664

List price of bicycle = ₹ 1,600

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%

∴ 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

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.

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.= ySales 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

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

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 = ₹ 1,800Expenditure = ₹ 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