Profit and Loss, Discount and Tax — Exercise 7(C)

The marked price of a refrigerator is ₹ 16,450. The shopkeeper offers an off-season discount of 16% on it. Find its selling price.

Answer

Given:

Marked price = ₹ 16,450, Discount % = 16%

Discount = 16% of M.P.

= 16% of ₹ 16,450

= ₹ $\Big(\dfrac{16}{100} \times 16450\Big)$

= ₹ 2,632.

S.P. of the refrigerator = M.P. - Discount = ₹ (16,450 - 2,632) = ₹ 13,818.

Hence, the selling price of the refrigerator is ₹ 13,818.

The price of a sweater was slashed down by a shopkeeper from ₹ 850 to ₹ 731. Find the rate of discount given by him.

Answer

Given:

M.P. = ₹ 850, S.P. = ₹ 731

Discount given = M.P. - S.P. = ₹ (850 - 731) = ₹ 119.

Rate of discount = $\Big(\dfrac{\text{Discount}}{\text{M.P.}} \times 100\Big)$%

= $\Big(\dfrac{119}{850} \times 100\Big)$%

= $\dfrac{11900}{850}$%

= 14%

Hence, the rate of discount given by him is 14%.

Find the rate of discount being given on a mini toy-gun whose selling price is ₹ 345 after deducting a discount of ₹ 30 on its marked price.

Answer

Given:

S.P. = ₹ 345, Discount = ₹ 30

M.P. = S.P. + Discount = ₹ (345 + 30) = ₹ 375.

Rate of discount = $\Big(\dfrac{\text{Discount}}{\text{M.P.}} \times 100\Big)$%

= $\Big(\dfrac{30}{375} \times 100\Big)$%

= $\dfrac{3000}{375}$%

= 8%

Hence, the rate of discount is 8%.

After allowing a discount of 15%, a baby-suit was sold for ₹ 1,156. Find its marked price.

Answer

Given:

Discount % = 15%, S.P. = ₹ 1,156

Let the marked price be ₹ $x$.

Discount = 15% of ₹ $x = ₹ \dfrac{15x}{100}$.

$\text{S.P.} = \text{M.P.} - \text{Discount} \\[1em] \Rightarrow 1156 = x - \dfrac{15x}{100} \\[1em] \Rightarrow 1156 = \dfrac{85x}{100} \\[1em] \Rightarrow x = \dfrac{1156 \times 100}{85} \\[1em] \Rightarrow x = 1360$

Hence, the marked price of the baby-suit is ₹ 1,360.

A calculator was bought for ₹ 435 after getting a discount of 13%. Find the marked price of the calculator.

Answer

Given:

Discount % = 13%, S.P. = ₹ 435

Let the marked price be ₹ $x$.

Discount = 13% of ₹ $x = ₹ \dfrac{13x}{100}$.

$\text{S.P.} = \text{M.P.} - \text{Discount} \\[1em] \Rightarrow 435 = x - \dfrac{13x}{100} \\[1em] \Rightarrow 435 = \dfrac{87x}{100} \\[1em] \Rightarrow x = \dfrac{435 \times 100}{87} \\[1em] \Rightarrow x = 500$

Hence, the marked price of the calculator is ₹ 500.

A dealer marked his goods 35% above cost price and allowed a discount of 20% on the marked price. Find his gain or loss per cent.

Answer

Let the cost price of the goods be ₹ 100.

Then, its marked price = ₹ $\Big(100 + \dfrac{35}{100} \times 100\Big)$ = ₹ (100 + 35) = ₹ 135.

Discount = 20% of M.P. = 20% of ₹ 135 = ₹ $\Big(\dfrac{20}{100} \times 135\Big)$ = ₹ 27.

Selling price = M.P. - Discount = ₹ (135 - 27) = ₹ 108.

Since S.P. > C.P., so there is a gain.

Gain = S.P. - C.P. = ₹ (108 - 100) = ₹ 8.

On a cost price of ₹ 100, the gain is ₹ 8.

Gain % = $\Big(\dfrac{\text{Gain}}{\text{C.P.}} \times 100\Big)$%

= $\Big(\dfrac{8}{100} \times 100\Big)$%

= 8%

Hence, the dealer gains 8%.

An article was marked 40% above cost price and a discount of 35% was given on its marked price. Find the gain or loss per cent made by the shopkeeper.

Answer

Let the cost price of the article be ₹ 100.

Then, its marked price = ₹ $\Big(100 + \dfrac{40}{100} \times 100\Big)$ = ₹ (100 + 40) = ₹ 140.

Discount = 35% of M.P. = 35% of ₹ 140 = ₹ $\Big(\dfrac{35}{100} \times 140\Big)$ = ₹ 49.

Selling price = M.P. - Discount = ₹ (140 - 49) = ₹ 91.

Since C.P. > S.P., so there is a loss.

Loss = C.P. - S.P. = ₹ (100 - 91) = ₹ 9.

On a cost price of ₹ 100, the loss is ₹ 9.

Loss % = $\Big(\dfrac{\text{Loss}}{\text{C.P.}} \times 100\Big)$%

= $\Big(\dfrac{9}{100} \times 100\Big)$%

= 9%

Hence, the shopkeeper makes a loss of 9%.

A dealer purchased a washing machine for ₹ 7,660. After allowing a discount of 12% on its marked price, he gains 10%. Find the marked price.

Answer

Given:

C.P. = ₹ 7,660, Gain % = 10%, Discount % = 12%

$\text{S.P.} = \dfrac{(100 + \text{gain percentage})}{100} \times \text{C.P.} \\[1em] = ₹ \Big(\dfrac{100 + 10}{100} \times 7660\Big) \\[1em] = ₹ \Big(\dfrac{110}{100} \times 7660\Big) \\[1em] = ₹ 8,426$

Let the marked price be ₹ $x$.

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

$\text{S.P.} = \text{M.P.} - \text{Discount} \\[1em] \Rightarrow 8426 = x - \dfrac{12x}{100} \\[1em] \Rightarrow 8426 = \dfrac{88x}{100} \\[1em] \Rightarrow x = \dfrac{8426 \times 100}{88} \\[1em] \Rightarrow x = 9575$

Hence, the marked price of the washing machine is ₹ 9,575.

A shopkeeper bought a sewing machine for ₹ 3,750. After allowing a discount of 10% on its marked price, he gains 26%. Find the marked price of the sewing machine.

Answer

Given:

C.P. = ₹ 3,750, Gain % = 26%, Discount % = 10%

$\text{S.P.} = \dfrac{(100 + \text{gain percentage})}{100} \times \text{C.P.} \\[1em] = ₹ \Big(\dfrac{100 + 26}{100} \times 3750\Big) \\[1em] = ₹ \Big(\dfrac{126}{100} \times 3750\Big) \\[1em] = ₹ 4725$

Let the marked price be ₹ $x$.

Discount = 10% of ₹ $x = ₹ \dfrac{10x}{100}$.

$\text{S.P.} = \text{M.P.} - \text{Discount} \\[1em] \Rightarrow 4725 = x - \dfrac{10x}{100} \\[1em] \Rightarrow 4725 = \dfrac{90x}{100} \\[1em] \Rightarrow x = \dfrac{4725 \times 100}{90} \\[1em] \Rightarrow x = 5250$

Hence, the marked price of the sewing machine is ₹ 5,250.

After allowing a discount of 10% on the marked price, a trader still makes a profit of 17%. By what per cent is the marked price above cost price?

Answer

Let the cost price be ₹ 100.

Since the profit is 17%, S.P. = ₹ (100 + 17) = ₹ 117.

Let the marked price be ₹ $x$.

Discount = 10% of ₹ $x$, so S.P. = 90% of M.P.

$\Rightarrow \dfrac{90x}{100} = 117 \\[1em] \Rightarrow x = \dfrac{117 \times 100}{90} \\[1em] \Rightarrow x = 130$

M.P. = ₹ 130 and C.P. = ₹ 100.

M.P. is above C.P. by ₹ (130 - 100) = ₹ 30.

On a cost price of ₹ 100, the marked price is ₹ 30 above.

Required per cent = $\Big(\dfrac{\text{M.P.} - \text{C.P.}}{\text{C.P.}} \times 100\Big)$%

= $\Big(\dfrac{30}{100} \times 100\Big)$%

= 30%

Hence, the marked price is 30% above the cost price.

After allowing a discount of 12% on the marked price, a shopkeeper still gains 21%. By what per cent is the marked price above cost price?

Answer

Let the cost price be ₹ 100.

Since the gain is 21%, S.P. = ₹ (100 + 21) = ₹ 121.

Let the marked price be ₹ $x$.

Discount = 12% of ₹ $x$, so S.P. = 88% of M.P.

$\Rightarrow \dfrac{88x}{100} = 121 \\[1em] \Rightarrow x = \dfrac{121 \times 100}{88} \\[1em] \Rightarrow x = \dfrac{275}{2} \\[1em] \Rightarrow x = 137.50$

M.P. = ₹ 137.50 and C.P. = ₹ 100.

M.P. is above C.P. by ₹ (137.50 - 100) = ₹ 37.50.

On a cost price of ₹ 100, the marked price is ₹ 37.50 above.

Required per cent = $\Big(\dfrac{\text{M.P.} - \text{C.P.}}{\text{C.P.}} \times 100\Big)$%

= $\Big(\dfrac{37.50}{100} \times 100\Big)$%

= $37\dfrac{1}{2}$%

Hence, the marked price is $\mathbf{37\dfrac{1}{2}}$% above the cost price.

Find a single discount equivalent to two successive discounts of 20% and 10%.

Answer

Let the marked price be ₹ 100.

First discount = 20% of ₹ 100 = ₹ $\Big(\dfrac{20}{100} \times 100\Big)$ = ₹ 20.

Price after the first discount = ₹ (100 - 20) = ₹ 80.

Second discount = 10% of ₹ 80 = ₹ $\Big(\dfrac{10}{100} \times 80\Big)$ = ₹ 8.

Price after the second discount = ₹ (80 - 8) = ₹ 72.

Net discount = ₹ (100 - 72) = ₹ 28.

On a marked price of ₹ 100, the discount is ₹ 28.

Discount % = $\Big(\dfrac{\text{Discount}}{\text{M.P.}} \times 100\Big)$%

= $\Big(\dfrac{28}{100} \times 100\Big)$%

= 28%

Hence, the single discount equivalent to the given successive discounts is 28%.

Find a single discount equivalent to two successive discounts of 40% and 5%.

Answer

Let the marked price be ₹ 100.

First discount = 40% of ₹ 100 = ₹ $\Big(\dfrac{40}{100} \times 100\Big)$ = ₹ 40.

Price after the first discount = ₹ (100 - 40) = ₹ 60.

Second discount = 5% of ₹ 60 = ₹ $\Big(\dfrac{5}{100} \times 60\Big)$ = ₹ 3.

Price after the second discount = ₹ (60 - 3) = ₹ 57.

Net discount = ₹ (100 - 57) = ₹ 43.

On a marked price of ₹ 100, the discount is ₹ 43.

Discount % = $\Big(\dfrac{\text{Discount}}{\text{M.P.}} \times 100\Big)$%

= $\Big(\dfrac{43}{100} \times 100\Big)$%

= 43%

Hence, the single discount equivalent to the given successive discounts is 43%.

Find a single discount equivalent to three successive discounts of 20%, 5% and 1%.

Answer

Let the marked price be ₹ 100.

First discount = 20% of ₹ 100 = ₹ $\Big(\dfrac{20}{100} \times 100\Big)$ = ₹ 20.

Price after the first discount = ₹ (100 - 20) = ₹ 80.

Second discount = 5% of ₹ 80 = ₹ $\Big(\dfrac{5}{100} \times 80\Big)$ = ₹ 4.

Price after the second discount = ₹ (80 - 4) = ₹ 76.

Third discount = 1% of ₹ 76 = ₹ $\Big(\dfrac{1}{100} \times 76\Big)$ = ₹ 0.76.

Price after the third discount = ₹ (76 - 0.76) = ₹ 75.24.

Net discount = ₹ (100 - 75.24) = ₹ 24.76.

On a marked price of ₹ 100, the discount is ₹ 24.76.

Discount % = $\Big(\dfrac{\text{Discount}}{\text{M.P.}} \times 100\Big)$%

= $\Big(\dfrac{24.76}{100} \times 100\Big)$%

= 24.76%

Hence, the single discount equivalent to the given successive discounts is 24.76%.

The marked price of a watch is ₹ 1,375. If tax is charged at the rate of 4%, find the total cost of the watch.

Answer

Given:

Marked price of the watch = ₹ 1,375, Rate of tax = 4%

Tax = 4% of ₹ 1,375 = ₹ $\Big(\dfrac{4}{100} \times 1375\Big)$ = ₹ 55.

Total amount to be paid = ₹ (1,375 + 55) = ₹ 1,430.

Hence, the total cost of the watch is ₹ 1,430.

Ravi buys a bicycle with a marked price of ₹ 12,500. He gets a rebate of 10% on it. After getting the rebate, tax is charged at the rate of 6%. Find the amount he will have to pay for the bicycle.

Answer

Given:

Marked price of the bicycle = ₹ 12,500, Rebate = 10%, Rate of tax = 6%

Rebate = 10% of ₹ 12,500 = ₹ $\Big(\dfrac{10}{100} \times 12500\Big)$ = ₹ 1,250.

Sale price of the bicycle = ₹ (12,500 - 1,250) = ₹ 11,250.

Tax = 6% of ₹ 11,250 = ₹ $\Big(\dfrac{6}{100} \times 11250\Big)$ = ₹ 675.

Total amount paid by Ravi = ₹ (11,250 + 675) = ₹ 11,925.

Hence, Ravi will have to pay ₹ 11,925 for the bicycle.

The list price of a washing machine is ₹ 25,000 and the shopkeeper gives a discount of 12% on the list price. On the remaining amount, he charges a tax of 10%.

Find:

(i) the amount of tax, a customer has to pay, and

(ii) the final price he has to pay for the washing machine.

Answer

Given:

List price of the washing machine = ₹ 25,000, Discount = 12%, Rate of tax = 10%

Discount = 12% of ₹ 25,000 = ₹ $\Big(\dfrac{12}{100} \times 25000\Big)$ = ₹ 3,000.

Sale price of the washing machine = ₹ (25,000 - 3,000) = ₹ 22,000.

(i) Tax = 10% of ₹ 22,000 = ₹ $\Big(\dfrac{10}{100} \times 22000\Big)$ = ₹ 2,200.

Hence, the amount of tax the customer has to pay is ₹ 2,200.

(ii) Final price = ₹ (22,000 + 2,200) = ₹ 24,200.

Hence, the final price he has to pay for the washing machine is ₹ 24,200.

Reena purchased a face cream for ₹ 113.40 including tax. If the printed price of the face cream is ₹ 105, find the rate of tax on it.

Answer

Given:

Printed price of the face cream = ₹ 105, Price paid including tax = ₹ 113.40

Tax = ₹ (113.40 - 105) = ₹ 8.40.

Rate of tax = $\Big(\dfrac{\text{Tax}}{\text{Printed price}} \times 100\Big)$%

= $\Big(\dfrac{8.40}{105} \times 100\Big)$%

= $\dfrac{840}{105}$%

= 8%

Hence, the rate of tax on the face cream is 8%.

Vivek purchased a laptop for ₹ 34,164, which includes 10% rebate on the marked price and then 4% tax on the remaining price. Find the marked price of the laptop.

Answer

Let the marked price of the laptop be ₹ $x$.

Rebate = 10% of ₹ $x = ₹ \dfrac{10x}{100}$.

Price after rebate = ₹ $\Big(x - \dfrac{10x}{100}\Big) = ₹ \dfrac{90x}{100} = ₹ \dfrac{9x}{10}$.

Tax = 4% of ₹ $\dfrac{9x}{10} = ₹ \Big(\dfrac{4}{100} \times \dfrac{9x}{10}\Big) = ₹ \dfrac{9x}{250}$.

Total price paid = ₹ $\Big(\dfrac{9x}{10} + \dfrac{9x}{250}\Big) = ₹ \dfrac{225x + 9x}{250} = ₹ \dfrac{234x}{250}$.

$\Rightarrow \dfrac{234x}{250} = 34164 \\[1em] \Rightarrow x = \dfrac{34164 \times 250}{234} \\[1em] \Rightarrow x = \dfrac{8541000}{234} \\[1em] \Rightarrow x = 36500$

Hence, the marked price of the laptop is ₹ 36,500.

Tanya buys an electric iron for ₹ 712.80, which includes two successive discounts of 10% and 4% respectively on the marked price and then 10% tax on the remaining price. Find the marked price of the electric iron.

Answer

Let the marked price be ₹ 100.

$\text{Price after the two discounts} = ₹ \Big[\Big(1 - \dfrac{10}{100}\Big)\Big(1 - \dfrac{4}{100}\Big) \times 100\Big] \\[1em] = ₹ \Big(\dfrac{90}{100} \times \dfrac{96}{100} \times 100\Big) \\[1em] = ₹ 86.40$

Tax = 10% of ₹ 86.40 = ₹ $\Big(\dfrac{10}{100} \times 86.40\Big)$ = ₹ 8.64.

S.P. = ₹ (86.40 + 8.64) = ₹ 95.04.

If the S.P. is ₹ 95.04, then M.P. = ₹ 100.

$\Rightarrow \text{If the S.P. is ₹ 712.80, then M.P.} = ₹ \Big(\dfrac{100}{95.04} \times 712.80\Big) \\[1em] \Rightarrow \text{M.P.} = ₹ \dfrac{71280}{95.04} \\[1em] \Rightarrow \text{M.P.} = ₹ 750$

Hence, the marked price of the electric iron is ₹ 750.

The price of a food processor inclusive of tax of 5% is ₹ 6,930. If the tax is increased to 8%, how much more does the customer pay for it?

Answer

Given:

Price of the food processor inclusive of 5% tax = ₹ 6,930

Let the sale price of the food processor be ₹ $x$.

Tax = 5% of ₹ $x = ₹ \dfrac{5x}{100}$.

$\Rightarrow x + \dfrac{5x}{100} = 6930 \\[1em] \Rightarrow \dfrac{105x}{100} = 6930 \\[1em] \Rightarrow x = \dfrac{6930 \times 100}{105} \\[1em] \Rightarrow x = 6600$

When the tax is increased to 8%,

New tax = 8% of ₹ 6,600 = ₹ $\Big(\dfrac{8}{100} \times 6600\Big)$ = ₹ 528.

New price of the food processor = ₹ (6,600 + 528) = ₹ 7,128.

Extra amount paid = ₹ (7,128 - 6,930) = ₹ 198.

Hence, the customer pays ₹ 198 more for the food processor.

The price of a laser printer including 7% tax, is ₹ 17,334. How much less does a customer pay for it, if the tax on it is reduced to 4%?

Answer

Given:

Price of the laser printer inclusive of 7% tax = ₹ 17,334

Let the sale price of the laser printer be ₹ $x$.

Tax = 7% of ₹ $x = ₹ \dfrac{7x}{100}$.

$\Rightarrow x + \dfrac{7x}{100} = 17334 \\[1em] \Rightarrow \dfrac{107x}{100} = 17334 \\[1em] \Rightarrow x = \dfrac{17334 \times 100}{107} \\[1em] \Rightarrow x = 16200$

When the tax is reduced to 4%,

New tax = 4% of ₹ 16,200 = ₹ $\Big(\dfrac{4}{100} \times 16200\Big)$ = ₹ 648.

New price of the laser printer = ₹ (16,200 + 648) = ₹ 16,848.

Amount saved = ₹ (17,334 - 16,848) = ₹ 486.

Hence, the customer pays ₹ 486 less for the laser printer.