Percentage and its Applications — Exercise 7.2

Find the profit or loss percentage, when:

(i) C.P. = ₹400, S.P. = ₹468

(ii) C.P. = ₹13,600, S.P. = ₹12,104

Answer

(i) C.P. of the article = ₹400

S.P. of the article = ₹468

As S.P. > C.P., there is a profit.

Profit = S.P. - C.P.

= ₹468 - ₹400

= ₹68

Profit percentage = $\dfrac{\text{Profit}}{\text{C.P.}} \times 100$%

= $\dfrac{68}{400} \times 100$%

= $\dfrac{6800}{400}$%

= 17%

Hence, there is a profit of 17%.

(ii) C.P. of the article = ₹13,600

S.P. of the article = ₹12,104

As S.P. < C.P., there is a loss.

Loss = C.P. - S.P.

= ₹13,600 - ₹12,104

= ₹1,496

Loss percentage = $\dfrac{\text{Loss}}{\text{C.P.}} \times 100$%

= $\dfrac{1496}{13600} \times 100$%

= $\dfrac{149600}{13600}$%

= 11%

Hence, there is a loss of 11%.

By selling an article for ₹1,636.25, a dealer gains ₹96.25. Find his gain percentage.

Answer

Given:

S.P. of the article = ₹1,636.25

Gain = ₹96.25

C.P. of the article = S.P. - Gain

= ₹1,636.25 - ₹96.25

= ₹1,540

Gain percentage = $\dfrac{\text{Gain}}{\text{C.P.}} \times 100$%

= $\dfrac{96.25}{1540} \times 100$%

= $\dfrac{9625}{1540}$%

= 6.25%

Hence, the gain percentage is 6.25%.

By selling an article for ₹770, a man incurs a loss of ₹110. Find his loss percentage.

Answer

Given:

S.P. of the article = ₹770

Loss = ₹110

C.P. of the article = S.P. + Loss

= ₹770 + ₹110

= ₹880

Loss percentage = $\dfrac{\text{Loss}}{\text{C.P.}} \times 100$%

= $\dfrac{110}{880} \times 100$%

= $\dfrac{11000}{880}$%

= 12.5%

Hence, the loss percentage is 12.5%.

Rashida bought 25 dozen eggs at the rate of ₹48 per dozen. 30 eggs were broken in the transaction and she sold the remaining eggs at 5 rupee each. Find her gain or loss percentage.

Answer

Given:

Number of dozens of eggs bought = 25

Rate of buying = ₹48 per dozen

Number of eggs broken = 30

Selling rate of the remaining eggs = ₹5 each

Total number of eggs bought = 25 x 12 = 300

C.P. of 300 eggs = 25 x ₹48 = ₹1,200

Number of eggs left after breakage = 300 - 30 = 270

S.P. of 270 eggs = 270 x ₹5 = ₹1,350

As S.P. > C.P., there is a gain.

Gain = S.P. - C.P.

= ₹1,350 - ₹1,200

= ₹150

Gain percentage = $\dfrac{\text{Gain}}{\text{C.P.}} \times 100$%

= $\dfrac{150}{1200} \times 100$%

= $\dfrac{15000}{1200}$%

= 12.5%

Hence, Rashida made a gain of 12.5%.

The cost of an article was ₹20,000 and ₹1,400 were spent on its repairs. If it is sold for a profit of 20%, find the selling price of the article.

Answer

Given:

Cost of the article = ₹20,000

Overhead expenses on repairs = ₹1,400

Profit = 20%

Total C.P. of the article = Cost + Overheads

= ₹20,000 + ₹1,400

= ₹21,400

As the article is sold at a profit of 20%,

Profit = 20% of C.P.

S.P. of the article = C.P. + Profit

= C.P. + 20% of C.P.

= $\Big(1 + \dfrac{20}{100}\Big)$ of C.P.

In general,

S.P. = $\Big(1 + \dfrac{\text{Profit Percentage}}{100}\Big) \times$ C.P.

$\text{S.P. of the article} = \Big(1 + \dfrac{20}{100}\Big)\text{ of C.P.} \\[1em] = \dfrac{120}{100} \times 21400 \\[1em] = \dfrac{2568000}{100} \\[1em] = ₹25{,}680$

Hence, the selling price of the article is ₹25,680.

A shopkeeper buys 200 fans at ₹1,200 per fan. He spends ₹30 per fan on transportation. He also spends ₹4,000 on advertising. Then he sells all the fans at ₹1,350 per piece. Find his profit or loss. Also calculate it as a percentage.

Answer

Given:

Number of fans bought = 200

Cost of one fan = ₹1,200

Transportation cost per fan = ₹30

Advertising cost = ₹4,000

Selling price of one fan = ₹1,350

Cost of 200 fans = 200 x ₹1,200 = ₹2,40,000

Transportation cost of 200 fans = 200 x ₹30 = ₹6,000

Total C.P. of 200 fans = Cost + Transportation + Advertising

= ₹2,40,000 + ₹6,000 + ₹4,000

= ₹2,50,000

S.P. of 200 fans = 200 x ₹1,350 = ₹2,70,000

As S.P. > C.P., there is a profit.

Profit = S.P. - C.P.

= ₹2,70,000 - ₹2,50,000

= ₹20,000

Profit percentage = $\dfrac{\text{Profit}}{\text{C.P.}} \times 100$%

= $\dfrac{20000}{250000} \times 100$%

= $\dfrac{2000000}{250000}$%

= 8%

Hence, the shopkeeper made a profit of ₹20,000 and the profit percentage is 8%.

The cost price of an article is 90% of its selling price. Find his profit percentage.

Answer

Given:

C.P. of the article = 90% of its S.P.

Let the S.P. of the article be ₹$x$.

C.P. of the article = 90% of ₹$x$

= $\dfrac{90}{100} \times x$

= ₹$\dfrac{9x}{10}$

As S.P. > C.P., there is a profit.

Profit = S.P. - C.P.

$= ₹\Big(x - \dfrac{9x}{10}\Big) \\[1em] = ₹\dfrac{10x - 9x}{10} \\[1em] = ₹\dfrac{x}{10}$

Profit percentage = $\dfrac{\text{Profit}}{\text{C.P.}} \times 100$%

= $\dfrac{\dfrac{x}{10}}{\dfrac{9x}{10}} \times 100$%

= $\dfrac{x}{10} \times \dfrac{10}{9x} \times 100$%

= $\dfrac{100}{9}$%

= $11\dfrac{1}{9}$%

Hence, the profit percentage is $\mathbf{11\dfrac{1}{9}}$%.

Suresh bought ball pens at the rate of 4 for ₹35 and sold them at the rate of 5 for ₹58. Calculate

(i) his gain percentage.

(ii) the number of ball pens he should sell to earn a profit of ₹171.

Answer

Given:

C.P. of 4 ball pens = ₹35

S.P. of 5 ball pens = ₹58

(i) C.P. of 1 ball pen = ₹$\dfrac{35}{4}$

S.P. of 1 ball pen = ₹$\dfrac{58}{5}$

Gain on the sale of one ball pen = S.P. - C.P.

$= ₹\Big(\dfrac{58}{5} - \dfrac{35}{4}\Big) \\[1em] = ₹\dfrac{232 - 175}{20} \\[1em] = ₹\dfrac{57}{20}$

Gain percentage = $\dfrac{\text{Gain}}{\text{C.P.}} \times 100$%

= $\dfrac{\dfrac{57}{20}}{\dfrac{35}{4}} \times 100$%

= $\dfrac{57}{20} \times \dfrac{4}{35} \times 100$%

= $\dfrac{22800}{700}$%

= $\dfrac{228}{7}$%

= $32\dfrac{4}{7}$%

Hence, the gain percentage is $\mathbf{32\dfrac{4}{7}}$%.

(ii) Number of ball pens to be sold = $\dfrac{\text{Total profit}}{\text{Profit on one ball pen}}$

$= \dfrac{171}{\dfrac{57}{20}} \\[1em] = 171 \times \dfrac{20}{57} \\[1em] = \dfrac{3420}{57} \\[1em] = 60$

Hence, he should sell 60 ball pens to earn a profit of ₹171.

A vendor buys bananas at 3 for a rupee and sells at 4 for a rupee. Find his profit or loss percentage.

Answer

Given:

C.P. of 3 bananas = ₹1

S.P. of 4 bananas = ₹1

C.P. of 1 banana = ₹$\dfrac{1}{3}$

S.P. of 1 banana = ₹$\dfrac{1}{4}$

As S.P. < C.P., there is a loss.

Loss on the sale of one banana = C.P. - S.P.

$= ₹\Big(\dfrac{1}{3} - \dfrac{1}{4}\Big) \\[1em] = ₹\dfrac{4 - 3}{12} \\[1em] = ₹\dfrac{1}{12}$

Loss percentage = $\dfrac{\text{Loss}}{\text{C.P.}} \times 100$%

= $\dfrac{\dfrac{1}{12}}{\dfrac{1}{3}} \times 100$%

= $\dfrac{1}{12} \times \dfrac{3}{1} \times 100$%

= $\dfrac{300}{12}$%

= 25%

Hence, the vendor made a loss of 25%.

A shopkeeper buys a certain number of geometry boxes. If the selling price of 5 geometry boxes is equal to the cost price of 7 geometry boxes, find his profit or loss percentage.

Answer

Given:

S.P. of 5 geometry boxes = C.P. of 7 geometry boxes

Let the cost price of one geometry box be ₹$x$.

C.P. of 7 geometry boxes = ₹$7x$

It is given that S.P. of 5 geometry boxes = C.P. of 7 geometry boxes

∴ S.P. of 5 geometry boxes = ₹$7x$

∴ S.P. of one geometry box = ₹$\dfrac{7x}{5}$

As the cost price of one geometry box is ₹$x$ and the selling price of one geometry box is ₹$\dfrac{7x}{5}$, the shopkeeper makes a profit.

Profit on selling one geometry box = S.P. - C.P.

$= ₹\Big(\dfrac{7x}{5} - x\Big) \\[1em] = ₹\dfrac{7x - 5x}{5} \\[1em] = ₹\dfrac{2x}{5}$

Profit percentage = $\dfrac{\text{Profit}}{\text{C.P.}} \times 100$%

= $\dfrac{\dfrac{2x}{5}}{x} \times 100$%

= $\dfrac{2x}{5} \times \dfrac{1}{x} \times 100$%

= $\dfrac{200}{5}$%

= 40%

Hence, the shopkeeper made a profit of 40%.

Find the selling price, when:

(i) cost price = ₹2,360, profit = 8%

(ii) cost price = ₹380, loss = 7.5%

Answer

(i) C.P. of the article = ₹2,360

Profit = 8%

S.P. = $\Big(1 + \dfrac{\text{Profit Percentage}}{100}\Big) \times$ C.P.

$\text{S.P. of the article} = \Big(1 + \dfrac{8}{100}\Big)\text{ of C.P.} \\[1em] = \dfrac{108}{100} \times 2360 \\[1em] = \dfrac{254880}{100} \\[1em] = ₹2{,}548.80$

Hence, the selling price of the article is ₹2,548.80.

(ii) C.P. of the article = ₹380

Loss = 7.5%

S.P. = $\Big(1 - \dfrac{\text{Loss Percentage}}{100}\Big) \times$ C.P.

$\text{S.P. of the article} = \Big(1 - \dfrac{7.5}{100}\Big)\text{ of C.P.} \\[1em] = \dfrac{92.5}{100} \times 380 \\[1em] = \dfrac{35150}{100} \\[1em] = ₹351.50$

Hence, the selling price of the article is ₹351.50.

A dealer bought a number of eggs at ₹36 a dozen and sold them at 50% profit. Find the selling price per egg.

Answer

Given:

C.P. of one dozen eggs = ₹36

Profit = 50%

S.P. = $\Big(1 + \dfrac{\text{Profit Percentage}}{100}\Big) \times$ C.P.

$\text{S.P. of one dozen eggs} = \Big(1 + \dfrac{50}{100}\Big)\text{ of C.P.} \\[1em] = \dfrac{150}{100} \times 36 \\[1em] = \dfrac{5400}{100} \\[1em] = ₹54$

S.P. of one egg = $\dfrac{54}{12}$

= ₹4.50

Hence, the selling price per egg is ₹4.50.

Mr. Ghosh purchased wrist watches worth ₹60,000. He sold one-third of them at a profit of 30%, one-third at a profit of 20% and the remaining at a loss of 5%. Calculate his overall profit or loss percentage.

Answer

Given:

Total C.P. of the wrist watches = ₹60,000

One-third sold at a profit of 30%, one-third at a profit of 20% and the remaining one-third at a loss of 5%.

C.P. of one-third of the wrist watches = $\dfrac{1}{3} \times 60000$ = ₹20,000

S.P. = $\Big(1 + \dfrac{\text{Profit Percentage}}{100}\Big) \times$ C.P.

S.P. = $\Big(1 - \dfrac{\text{Loss Percentage}}{100}\Big) \times$ C.P.

S.P. of the first one-third at a profit of 30% = $\Big(1 + \dfrac{30}{100}\Big) \times 20000$

= $\dfrac{130}{100} \times 20000$

= ₹26,000

S.P. of the second one-third at a profit of 20% = $\Big(1 + \dfrac{20}{100}\Big) \times 20000$

= $\dfrac{120}{100} \times 20000$

= ₹24,000

S.P. of the remaining one-third at a loss of 5% = $\Big(1 - \dfrac{5}{100}\Big) \times 20000$

= $\dfrac{95}{100} \times 20000$

= ₹19,000

Total S.P. of all the wrist watches = ₹26,000 + ₹24,000 + ₹19,000 = ₹69,000

As S.P. > C.P., there is a profit.

Profit = S.P. - C.P.

= ₹69,000 - ₹60,000

= ₹9,000

Profit percentage = $\dfrac{\text{Profit}}{\text{C.P.}} \times 100$%

= $\dfrac{9000}{60000} \times 100$%

= $\dfrac{900000}{60000}$%

= 15%

Hence, Mr. Ghosh made an overall profit of 15%.

A laptop and a mobile phone were bought for ₹40,000 and ₹24,000 respectively. The shopkeeper made a profit of 8% on laptop and a loss of 12% on mobile phone. Find his gain or loss percent on the whole transaction.

Answer

Given:

C.P. of the laptop = ₹40,000, profit on laptop = 8%

C.P. of the mobile phone = ₹24,000, loss on mobile phone = 12%

S.P. = $\Big(1 + \dfrac{\text{Profit Percentage}}{100}\Big) \times$ C.P.

$\text{S.P. of the laptop} = \Big(1 + \dfrac{8}{100}\Big) \times 40000 \\[1em] = \dfrac{108}{100} \times 40000 \\[1em] = ₹43{,}200$

S.P. = $\Big(1 - \dfrac{\text{Loss Percentage}}{100}\Big) \times$ C.P.

$\text{S.P. of the mobile phone} = \Big(1 - \dfrac{12}{100}\Big) \times 24000 \\[1em] = \dfrac{88}{100} \times 24000 \\[1em] = ₹21{,}120$

Total C.P. = ₹40,000 + ₹24,000 = ₹64,000

Total S.P. = ₹43,200 + ₹21,120 = ₹64,320

As S.P. > C.P., there is a gain.

Gain = S.P. - C.P.

= ₹64,320 - ₹64,000

= ₹320

Gain percentage = $\dfrac{\text{Gain}}{\text{C.P.}} \times 100$%

= $\dfrac{320}{64000} \times 100$%

= $\dfrac{32000}{64000}$%

= 0.5%

Hence, the shopkeeper made a gain of 0.5% on the whole transaction.

Salman bought 40 chairs at ₹900 each. He sold one-fourth of them at a loss of 8%. At what price each must he sell the remaining chairs so as to gain 10% on the whole deal?

Answer

Given:

Number of chairs bought = 40

C.P. of each chair = ₹900

One-fourth of the chairs sold at a loss of 8%

Desired gain on the whole deal = 10%

C.P. of all the 40 chairs = 40 x ₹900 = ₹36,000

S.P. = $\Big(1 + \dfrac{\text{Gain Percentage}}{100}\Big) \times$ C.P.

S.P. of all the chairs to gain 10% = $\Big(1 + \dfrac{10}{100}\Big) \times 36000$

= $\dfrac{110}{100} \times 36000$

= ₹39,600

One-fourth of all the chairs = $\dfrac{1}{4} \times 40$ = 10

C.P. of 10 chairs = 10 x ₹900 = ₹9,000

As these chairs are sold at a loss of 8%,

S.P. = $\Big(1 - \dfrac{\text{Loss Percentage}}{100}\Big) \times$ C.P.

$\text{S.P. of these 10 chairs} = \Big(1 - \dfrac{8}{100}\Big) \times 9000 \\[1em] = \dfrac{92}{100} \times 9000 \\[1em] = ₹8{,}280$

Number of remaining chairs = 40 - 10 = 30

S.P. of the remaining 30 chairs = ₹39,600 - ₹8,280 = ₹31,320

S.P. of each of the remaining chairs = $\dfrac{31320}{30}$

= ₹1,044

Hence, he must sell each of the remaining chairs at ₹1,044.

A shopkeeper sold two electronic gadgets for ₹44,000 each. The shopkeeper made a loss of 12% on one and a profit of 10% on the other. Find his overall gain or loss.

Answer

Given:

S.P. of each gadget = ₹44,000

Loss on the first gadget = 12%

Profit on the second gadget = 10%

For the first gadget :

S.P. = ₹44,000, loss = 12%

S.P. = $\Big(1 - \dfrac{\text{Loss Percentage}}{100}\Big) \times$ C.P.

$\Rightarrow 44000 = \Big(1 - \dfrac{12}{100}\Big)\text{ of C.P.} \\[1em] \Rightarrow 44000 = \dfrac{88}{100}\text{ of C.P.} \\[1em] \Rightarrow \text{C.P.} = \dfrac{44000 \times 100}{88} \\[1em] \Rightarrow \text{C.P.} = ₹50{,}000$

For the second gadget :

S.P. = ₹44,000, profit = 10%

S.P. = $\Big(1 + \dfrac{\text{Profit Percentage}}{100}\Big) \times$ C.P.

$\Rightarrow 44000 = \Big(1 + \dfrac{10}{100}\Big)\text{ of C.P.} \\[1em] \Rightarrow 44000 = \dfrac{110}{100}\text{ of C.P.} \\[1em] \Rightarrow \text{C.P.} = \dfrac{44000 \times 100}{110} \\[1em] \Rightarrow \text{C.P.} = ₹40{,}000$

Total C.P. of both the gadgets = ₹50,000 + ₹40,000 = ₹90,000

Total S.P. of both the gadgets = ₹44,000 + ₹44,000 = ₹88,000

As S.P. < C.P., there is a loss.

Loss = C.P. - S.P.

= ₹90,000 - ₹88,000

= ₹2,000

Hence, the shopkeeper suffered an overall loss of ₹2,000.

The manufacturing price of a T.V. set is ₹24,000. The company sold it to a dealer at 20% profit and the dealer sold it to a customer at 12.5% profit. Find the price which the customer has to pay.

Answer

Given:

Manufacturing price of the T.V. set = ₹24,000

Profit of the company = 20%

Profit of the dealer = 12.5%

S.P. = $\Big(1 + \dfrac{\text{Profit Percentage}}{100}\Big) \times$ C.P.

$\text{S.P. of the T.V. set for the company} = \Big(1 + \dfrac{20}{100}\Big) \times 24000 \\[1em] = \dfrac{120}{100} \times 24000 \\[1em] = \dfrac{2880000}{100} \\[1em] = ₹28{,}800$

This becomes the C.P. of the T.V. set for the dealer.

$\text{S.P. of the T.V. set for the dealer} = \Big(1 + \dfrac{12.5}{100}\Big) \times 28800 \\[1em] = \dfrac{112.5}{100} \times 28800 \\[1em] = \dfrac{3240000}{100} \\[1em] = ₹32{,}400$

Hence, the customer has to pay ₹32,400 for the T.V. set.

Find the cost price, when:

(i) selling price = ₹450, loss = 10%

(ii) selling price = ₹690, profit = 15%

Answer

(i) S.P. of the article = ₹450, loss = 10%

S.P. = $\Big(1 - \dfrac{\text{Loss Percentage}}{100}\Big) \times$ C.P.

$\Rightarrow 450 = \Big(1 - \dfrac{10}{100}\Big)\text{ of C.P.} \\[1em] \Rightarrow 450 = \dfrac{90}{100}\text{ of C.P.} \\[1em] \Rightarrow \text{C.P.} = \dfrac{450 \times 100}{90} \\[1em] \Rightarrow \text{C.P.} = \dfrac{45000}{90} \\[1em] \Rightarrow \text{C.P.} = ₹500$

Hence, the cost price of the article is ₹500.

(ii) S.P. of the article = ₹690, profit = 15%

S.P. = $\Big(1 + \dfrac{\text{Profit Percentage}}{100}\Big) \times$ C.P.

$\Rightarrow 690 = \Big(1 + \dfrac{15}{100}\Big)\text{ of C.P.} \\[1em] \Rightarrow 690 = \dfrac{115}{100}\text{ of C.P.} \\[1em] \Rightarrow \text{C.P.} = \dfrac{690 \times 100}{115} \\[1em] \Rightarrow \text{C.P.} = \dfrac{69000}{115} \\[1em] \Rightarrow \text{C.P.} = ₹600$

Hence, the cost price of the article is ₹600.

By selling a shoe rack for ₹3,920, a shopkeeper would gain 12%. If it is sold for ₹4,375, find his gain or loss percentage.

Answer

Given:

S.P. of the shoe rack = ₹3,920, gain = 12%

New S.P. of the shoe rack = ₹4,375

S.P. = $\Big(1 + \dfrac{\text{Gain Percentage}}{100}\Big) \times$ C.P.

$\Rightarrow 3920 = \Big(1 + \dfrac{12}{100}\Big)\text{ of C.P.} \\[1em] \Rightarrow 3920 = \dfrac{112}{100}\text{ of C.P.} \\[1em] \Rightarrow \text{C.P.} = \dfrac{3920 \times 100}{112} \\[1em] \Rightarrow \text{C.P.} = \dfrac{392000}{112} \\[1em] \Rightarrow \text{C.P.} = ₹3{,}500$

Now the shoe rack is sold for ₹4,375.

As S.P. > C.P., there is a gain.

Gain = S.P. - C.P.

= ₹4,375 - ₹3,500

= ₹875

Gain percentage = $\dfrac{\text{Gain}}{\text{C.P.}} \times 100$%

= $\dfrac{875}{3500} \times 100$%

= $\dfrac{87500}{3500}$%

= 25%

Hence, the shopkeeper made a gain of 25%.

By selling a plastic coffee table at ₹1,334, a shopkeeper would suffer a loss of 8%. At how much amount should he sell it to make a profit of $12\dfrac{1}{2}$%?

Answer

Given:

S.P. of the plastic coffee table = ₹1,334, loss = 8%

Desired profit = $12\dfrac{1}{2}$% = 12.5%

S.P. = $\Big(1 - \dfrac{\text{Loss Percentage}}{100}\Big) \times$ C.P.

$\Rightarrow 1334 = \Big(1 - \dfrac{8}{100}\Big)\text{ of C.P.} \\[1em] \Rightarrow 1334 = \dfrac{92}{100}\text{ of C.P.} \\[1em] \Rightarrow \text{C.P.} = \dfrac{1334 \times 100}{92} \\[1em] \Rightarrow \text{C.P.} = \dfrac{133400}{92} \\[1em] \Rightarrow \text{C.P.} = ₹1{,}450$

Now C.P. = ₹1,450, profit = 12.5%,

S.P. = $\Big(1 + \dfrac{\text{Profit Percentage}}{100}\Big) \times$ C.P.

$\text{New S.P.} = \Big(1 + \dfrac{12.5}{100}\Big) \times 1450 \\[1em] = \dfrac{112.5}{100} \times 1450 \\[1em] = \dfrac{163125}{100} \\[1em] = ₹1{,}631.25$

Hence, he should sell the plastic coffee table for ₹1,631.25.

By selling a tie for ₹252, a shopkeeper gains 5%. At what price should he sell the tie to gain 35%?

Answer

Given:

S.P. of the tie = ₹252, gain = 5%

Desired gain = 35%

S.P. = $\Big(1 + \dfrac{\text{Gain Percentage}}{100}\Big) \times$ C.P.

$\Rightarrow 252 = \Big(1 + \dfrac{5}{100}\Big)\text{ of C.P.} \\[1em] \Rightarrow 252 = \dfrac{105}{100}\text{ of C.P.} \\[1em] \Rightarrow \text{C.P.} = \dfrac{252 \times 100}{105} \\[1em] \Rightarrow \text{C.P.} = \dfrac{25200}{105} \\[1em] \Rightarrow \text{C.P.} = ₹240$

Now C.P. = ₹240, gain = 35%,

$\text{New S.P.} = \Big(1 + \dfrac{35}{100}\Big) \times 240 \\[1em] = \dfrac{135}{100} \times 240 \\[1em] = \dfrac{32400}{100} \\[1em] = ₹324$

Hence, he should sell the tie for ₹324.

A shopkeeper sells a bag at 12% profit. If he had sold it for ₹39 more, he would have made 18% profit. Find the cost price of the bag for the shopkeeper.

Answer

Given:

Profit on selling the bag = 12%

On selling it for ₹39 more, profit = 18%

Let the cost price of the bag be ₹$x$.

S.P. = $\Big(1 + \dfrac{\text{Profit Percentage}}{100}\Big) \times$ C.P.

S.P. of the bag at 12% profit = $\Big(1 + \dfrac{12}{100}\Big)$ of ₹$x$

$= \dfrac{112}{100} \times x \\[1em] = ₹\dfrac{28x}{25}$

To obtain 18% profit,

$\text{S.P. of the bag} = \Big(1 + \dfrac{18}{100}\Big)\text{ of ₹}x \\[1em] = \dfrac{118}{100} \times x \\[1em] = ₹\dfrac{59x}{50}$

According to the given information,

$\Rightarrow \dfrac{59x}{50} = \dfrac{28x}{25} + 39 \\[1em] \Rightarrow \dfrac{59x}{50} - \dfrac{28x}{25} = 39 \\[1em] \Rightarrow \dfrac{59x - 56x}{50} = 39 \\[1em] \Rightarrow \dfrac{3x}{50} = 39 \\[1em] \Rightarrow x = \dfrac{39 \times 50}{3} \\[1em] \Rightarrow x = \dfrac{1950}{3} \\[1em] \Rightarrow x = 650$

Hence, the cost price of the bag is ₹650.

A shopkeeper sells a sweater at a loss of 5%. If he had sold it for ₹260 more, he would have made a profit of 15%. Calculate the purchase price of the sweater.

Answer

Given:

Loss on selling the sweater = 5%

On selling it for ₹260 more, profit = 15%

Let the purchase price of the sweater be ₹$x$.

S.P. = $\Big(1 - \dfrac{\text{Loss Percentage}}{100}\Big) \times$ C.P.

S.P. of the sweater at 5% loss = $\Big(1 - \dfrac{5}{100}\Big)$ of ₹$x$

$= \dfrac{95}{100} \times x \\[1em] = ₹\dfrac{19x}{20}$

To obtain 15% profit,

S.P. = $\Big(1 + \dfrac{\text{Profit Percentage}}{100}\Big) \times$ C.P.

$\text{S.P. of the sweater} = \Big(1 + \dfrac{15}{100}\Big)\text{ of ₹}x \\[1em] = \dfrac{115}{100} \times x \\[1em] = ₹\dfrac{23x}{20}$

According to the given information,

$\Rightarrow \dfrac{23x}{20} = \dfrac{19x}{20} + 260 \\[1em] \Rightarrow \dfrac{23x}{20} - \dfrac{19x}{20} = 260 \\[1em] \Rightarrow \dfrac{4x}{20} = 260 \\[1em] \Rightarrow \dfrac{x}{5} = 260 \\[1em] \Rightarrow x = 260 \times 5 \\[1em] \Rightarrow x = 1300$

Hence, the purchase price of the sweater is ₹1,300.

Diya sold her leather purse at 8% loss. If she had sold it for ₹150 more, she would have made 12% profit. Find the selling price of the purse.

Answer

Given:

Loss on selling the purse = 8%

On selling it for ₹150 more, profit = 12%

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

S.P. = $\Big(1 - \dfrac{\text{Loss Percentage}}{100}\Big) \times$ C.P.

S.P. of the purse at 8% loss = $\Big(1 - \dfrac{8}{100}\Big)$ of ₹$x$

$= \dfrac{92}{100} \times x \\[1em] = ₹\dfrac{23x}{25}$

To obtain 12% profit,

S.P. = $\Big(1 + \dfrac{\text{Profit Percentage}}{100}\Big) \times$ C.P.

$\text{S.P. of the purse} = \Big(1 + \dfrac{12}{100}\Big)\text{ of ₹}x \\[1em] = \dfrac{112}{100} \times x \\[1em] = ₹\dfrac{28x}{25}$

According to the given information,

$\Rightarrow \dfrac{28x}{25} = \dfrac{23x}{25} + 150 \\[1em] \Rightarrow \dfrac{28x}{25} - \dfrac{23x}{25} = 150 \\[1em] \Rightarrow \dfrac{5x}{25} = 150 \\[1em] \Rightarrow \dfrac{x}{5} = 150 \\[1em] \Rightarrow x = 150 \times 5 \\[1em] \Rightarrow x = 750$

∴ C.P. of the purse = ₹750

$\text{S.P. of the purse} = \dfrac{23x}{25} \\[1em] = \dfrac{23 \times 750}{25} \\[1em] = \dfrac{17250}{25} \\[1em] = ₹690$

Hence, the selling price of the purse is ₹690.