Percentage and its Applications — Exercise 7.4

Find the buying price of each of the following when 5% GST is added on the purchase of

(i) a spice packet of ₹50

(ii) 5 kg of refined oil at ₹150 per kg

Answer

Given:

Rate of GST = 5%

(i) Cost of the spice packet = ₹50

GST = 5% of ₹50

$= \dfrac{5}{100} \times 50 \\[1em] = \dfrac{250}{100} \\[1em] = ₹2.50$

Buying price = Cost of item + GST

= ₹50 + ₹2.50

= ₹52.50

Hence, the buying price of the spice packet is ₹52.50.

(ii) Cost of 5 kg of refined oil = 5 x ₹150 = ₹750

GST = 5% of ₹750

$= \dfrac{5}{100} \times 750 \\[1em] = \dfrac{3750}{100} \\[1em] = ₹37.50$

Buying price = Cost of item + GST

= ₹750 + ₹37.50

= ₹787.50

Hence, the buying price of 5 kg of refined oil is ₹787.50.

If 18% GST is included in the prices, find the original price of

(i) a small TV bought for ₹12,980

(ii) a shampoo bottle bought for ₹177

Answer

Given:

Rate of GST = 18%

(i) Buying price of the small TV = ₹12,980

Let the original price of the small TV be ₹$x$.

GST = 18% of ₹$x$ = ₹$\dfrac{18x}{100}$

Buying price = Original price + GST

$\Rightarrow 12980 = x + \dfrac{18x}{100} \\[1em] \Rightarrow 12980 = \dfrac{100x + 18x}{100} \\[1em] \Rightarrow 12980 = \dfrac{118x}{100} \\[1em] \Rightarrow x = \dfrac{12980 \times 100}{118} \\[1em] \Rightarrow x = \dfrac{1298000}{118} \\[1em] \Rightarrow x = 11000$

Hence, the original price of the small TV is ₹11,000.

(ii) Buying price of the shampoo bottle = ₹177

Let the original price of the shampoo bottle be ₹$x$.

GST = 18% of ₹$x$ = ₹$\dfrac{18x}{100}$

Buying price = Original price + GST

$\Rightarrow 177 = x + \dfrac{18x}{100} \\[1em] \Rightarrow 177 = \dfrac{100x + 18x}{100} \\[1em] \Rightarrow 177 = \dfrac{118x}{100} \\[1em] \Rightarrow x = \dfrac{177 \times 100}{118} \\[1em] \Rightarrow x = \dfrac{17700}{118} \\[1em] \Rightarrow x = 150$

Hence, the original price of the shampoo bottle is ₹150.

Utkarsh bought an AC for ₹41,472 including a GST of 28%. Find the price of AC before GST was added.

Answer

Given:

Buying price of the AC = ₹41,472

Rate of GST = 28%

Let the price of the AC before GST be ₹$x$.

GST = 28% of ₹$x$ = ₹$\dfrac{28x}{100}$

Buying price = Price before GST + GST

$\Rightarrow 41472 = x + \dfrac{28x}{100} \\[1em] \Rightarrow 41472 = \dfrac{100x + 28x}{100} \\[1em] \Rightarrow 41472 = \dfrac{128x}{100} \\[1em] \Rightarrow x = \dfrac{41472 \times 100}{128} \\[1em] \Rightarrow x = \dfrac{4147200}{128} \\[1em] \Rightarrow x = 32400$

Hence, the price of the AC before GST was added is ₹32,400.

Gaurav bought a shirt for ₹1,344 including GST. If the original price of the shirt is ₹1,200, find the rate of GST.

Answer

Given:

Buying price of the shirt = ₹1,344

Original price of the shirt = ₹1,200

GST = Buying price - Original price

= ₹1,344 - ₹1,200

= ₹144

Rate of GST = $\dfrac{\text{GST}}{\text{Original price}} \times 100$%

= $\dfrac{144}{1200} \times 100$%

= $\dfrac{14400}{1200}$%

= 12%

Hence, the rate of GST is 12%.

Anjali buys a purse for ₹560 including 12% GST. Find the new selling price of the purse if GST increases to 18%.

Answer

Given:

Buying price of the purse = ₹560 including 12% GST

New rate of GST = 18%

Let the original price of the purse be ₹$x$.

GST = 12% of ₹$x$ = ₹$\dfrac{12x}{100}$

Buying price = Original price + GST

$\Rightarrow 560 = x + \dfrac{12x}{100} \\[1em] \Rightarrow 560 = \dfrac{100x + 12x}{100} \\[1em] \Rightarrow 560 = \dfrac{112x}{100} \\[1em] \Rightarrow x = \dfrac{560 \times 100}{112} \\[1em] \Rightarrow x = \dfrac{56000}{112} \\[1em] \Rightarrow x = 500$

∴ Original price of the purse = ₹500

Now GST = 18% of ₹500

$= \dfrac{18}{100} \times 500 \\[1em] = \dfrac{9000}{100} \\[1em] = ₹90$

New selling price of the purse = Original price + GST

= ₹500 + ₹90

= ₹590

Hence, the new selling price of the purse is ₹590.

A painting is marked for ₹4,800 excluding GST. The shopkeeper offers 10% discount on it. If GST is 5%, find the amount paid by the customer to purchase the painting.

Answer

Given:

M.P. of the painting = ₹4,800 excluding GST

Rate of discount = 10%

Rate of GST = 5%

Discount = 10% of ₹4,800

$= \dfrac{10}{100} \times 4800 \\[1em] = \dfrac{48000}{100} \\[1em] = ₹480$

S.P. of the painting = M.P. - Discount

= ₹4,800 - ₹480

= ₹4,320

Now GST = 5% of ₹4,320

$= \dfrac{5}{100} \times 4320 \\[1em] = \dfrac{21600}{100} \\[1em] = ₹216$

Amount paid by the customer = S.P. + GST

= ₹4,320 + ₹216

= ₹4,536

Hence, the amount paid by the customer to purchase the painting is ₹4,536.

Amit goes to a shop to buy a solar cooker. The marked price is ₹7,840 excluding 12% GST. Amit bargains with shopkeeper and convinces him for ₹7,840 including GST as the final cost of the solar cooker. Find the amount reduced by the shopkeeper.

Answer

Given:

M.P. of the solar cooker = ₹7,840 excluding 12% GST

Final cost paid by Amit = ₹7,840 including GST

Let the reduced price of the solar cooker be ₹$x$.

GST = 12% of ₹$x$ = ₹$\dfrac{12x}{100}$

Amount paid by Amit = Reduced price + GST

$\Rightarrow 7840 = x + \dfrac{12x}{100} \\[1em] \Rightarrow 7840 = \dfrac{100x + 12x}{100} \\[1em] \Rightarrow 7840 = \dfrac{112x}{100} \\[1em] \Rightarrow x = \dfrac{7840 \times 100}{112} \\[1em] \Rightarrow x = \dfrac{784000}{112} \\[1em] \Rightarrow x = 7000$

∴ Reduced price of the solar cooker = ₹7,000

Amount reduced by the shopkeeper = ₹7,840 - ₹7,000 = ₹840

Hence, the amount reduced by the shopkeeper is ₹840.