## ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 7 Percentage Ex 7.4

Question 1.

Find the buying price of each of the following when 5% S.T. is added on the purchase of

(i) a towel of ₹50

(ii) 5 kg of flour at ₹15 per kg.

Solution:

(i) S.T. = 5%

Cost of towel = ₹50

Totals. S.T. = ₹ \(\frac{50 \times 5}{100}\) = ₹ 2.50

∴ Buying price = ₹50 + ₹2.50 = ₹52.50

(ii) Cost price of 5 kg of flour at the rate for ₹15 perkg = ₹15 × 5 = ₹75

Rate of S.T. = 5%

∴ Total tax = \(\frac{75 \times 5}{100}\) = ₹ \(\frac{375}{100}\) = ₹3.75

Total price of the flour = ₹75 + ₹3.75 = ₹8.75

Question 2.

If 8% VAT is included in the prices, find the original price of

(i) a TV bought for ₹ 13500

(ii) a shampoo bottle bought for ₹ 180.

Solution:

(i) Total price of a TV including VAT = ₹13500

Rate of VAT = 8%

Original price of TV = ₹ \(\frac{13500 \times 100}{100+8}\) = ₹ \(\frac{13500 \times 100}{108}\) = ₹12500

(ii) Total cost of shampoo bottle including VAT = ₹180

Rate of VAT = 8%

∴ Original price of shampoo = ₹ \(\frac{180 \times 100}{100+8}\)

= ₹ \(\frac{180 \times 100}{108}\) = ₹ \(\frac{500}{3}\)

= ₹ 166.67

Question 3.

Utkarsh bought an AC for ₹34992 including a VAT of 8%. Find the price of AC before VAT was added.

Solution:

Cost of AC including VAT = ₹34992

Rate of VAT charged = 8%

∴ Original price of AC = ₹ \(\frac{34992 \times 100}{100+8}\) = ₹ \(\frac{34992 \times 100}{108}\) = ₹ 32400

Question 4.

Gaurav bought a shirt for ₹ 1296 including VAT. If the original price of the shirt is ₹ 1 200, find the rate of VAT.

Solution:

Cost of shirt including VAT = ₹ 1296

Actual price of shirt = ₹120

∴ Amount of VAT = ₹ 1296 – 1200 = ₹ 96

Rate of VAT = \(\frac{\mathrm{VAT} \times 100}{\mathrm{C.P.}}\)

= \(\frac{96 \times 100}{1200}\) = 8%

Question 5.

Anjana buys a purse for ₹523.80 including 8% VAT. Find the new selling price of the purse if VAT increases to 10%.

Solution:

Total cost price of purse including VAT = ₹ 523.80

Rate of VAT = 8%

∴ Actual cost of the purse = ₹ \(\frac{523.80 \times 100}{100+8}\)

= ₹ \(\frac{523.80 \times 100}{108}\) = ₹ 485

New rate of VAT = 10%

Amount of VAT = ₹ 485 × \(\frac{10}{100}\) = ₹ \(\frac{4850}{100}\) = ₹48.50

∴ Total cost of the purse = ₹485 + ₹48.50 = ₹535.50

Question 6.

A wall hanging is marked for ₹4800. The shopkeeper offers 10% discount on it. If VAT is received 8% from the customer, find the amount paid by the customer to purchase the wall hanging.

Solution:

Marked price of wall hanging = ₹ 4800

Discount offered = 10%

∴ Net sale price = ₹ \(\frac{4800 \times(100-10)}{100}\)

= ₹\(\frac{4800 \times 90}{100}\) = ₹ 4320

Rate of VAT charged = 8%

Sale price including VAT

= ₹ 4665.60

Question 7.

Amit goes to a shop to buy a washing machine. The marked price of the washing machine is ₹ 10900 excluding9% VAT. Amit bargains with the shopkeeper and convinces him for ₹10900 including VAT as the final cost of the washing machine. Find the amount reduced by the shopkeeper.

Solution:

Marked price of washing machine = ₹ 10900

Rate of VAT = 9%

Let the reduced price of machine = ₹ x

VAT at the rate of 9% = ₹ x × \(\frac{9}{100}\) = ₹ \(\frac{9x}{100}\)

Amount paid = ₹ x + \(\frac{9x}{100}\) = \(\frac{109}{100}\) x

∴ \(\frac{109}{100}\)x = ₹ 10900 ⇒ x = \(\frac{10900 \times 100}{109}\)

∴ x = 10000

∴ Amount reduced by the shopkeeper = ₹10900 – 10000 = ₹900