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

Find the selling price when:

C.P. = ₹ 7,640, Gain = 15%

Answer

Given:

C.P. = ₹ 7,640, Gain % = 15%

$\text{S.P.} = \dfrac{(100 + \text{gain percentage})}{100} \times \text{C.P.} \\[1em] = ₹ \Big(\dfrac{100 + 15}{100} \times 7640\Big) \\[1em] = ₹ \Big(\dfrac{115}{100} \times 7640\Big) \\[1em] = ₹ 8786$

Hence, the selling price is ₹ 8,786.

Find the selling price when:

C.P. = ₹ 4,850, Loss = 12%

Answer

Given:

C.P. = ₹ 4,850, Loss % = 12%

$\text{S.P.} = \dfrac{(100 - \text{loss percentage})}{100} \times \text{C.P.} \\[1em] = ₹ \Big(\dfrac{100 - 12}{100} \times 4850\Big) \\[1em] = ₹ \Big(\dfrac{88}{100} \times 4850\Big) \\[1em] = ₹ 4268$

Hence, the selling price is ₹ 4,268.

Find the selling price when:

C.P. = ₹ 720, Loss = $8\dfrac{3}{4}$%

Answer

Given:

C.P. = ₹ 720, Loss % = $8\dfrac{3}{4}$% = $\dfrac{35}{4}$%

$\text{S.P.} = \dfrac{(100 - \text{loss percentage})}{100} \times \text{C.P.} \\[1em] = ₹ \Big(\dfrac{100 - \dfrac{35}{4}}{100} \times 720\Big) \\[1em] = ₹ \Big(\dfrac{365}{4 \times 100} \times 720\Big) \\[1em] = ₹ \Big(\dfrac{365}{400} \times 720\Big) \\[1em] = ₹ 657$

Hence, the selling price is ₹ 657.

Find the selling price when:

C.P. = ₹ 2,652, Gain = $16\dfrac{2}{3}$%

Answer

Given:

C.P. = ₹ 2,652, Gain % = $16\dfrac{2}{3}$% = $\dfrac{50}{3}$%

$\text{S.P.} = \dfrac{(100 + \text{gain percentage})}{100} \times \text{C.P.} \\[1em] = ₹ \Big(\dfrac{100 + \dfrac{50}{3}}{100} \times 2652\Big) \\[1em] = ₹ \Big(\dfrac{350}{3 \times 100} \times 2652\Big) \\[1em] = ₹ \Big(\dfrac{350}{300} \times 2652\Big) \\[1em] = ₹ 3094$

Hence, the selling price is ₹ 3,094.

Find the cost price when:

S.P. = ₹ 207, Gain = 15%

Answer

Given:

S.P. = ₹ 207, Gain % = 15%

$\text{C.P.} = \dfrac{100}{(100 + \text{gain percentage})} \times \text{S.P.} \\[1em] = ₹ \Big(\dfrac{100}{100 + 15} \times 207\Big) \\[1em] = ₹ \Big(\dfrac{100}{115} \times 207\Big) \\[1em] = ₹ 180$

Hence, the cost price is ₹ 180.

Find the cost price when:

S.P. = ₹ 448.20, Loss = 17%

Answer

Given:

S.P. = ₹ 448.20, Loss % = 17%

$\text{C.P.} = \dfrac{100}{(100 - \text{loss percentage})} \times \text{S.P.} \\[1em] = ₹ \Big(\dfrac{100}{100 - 17} \times 448.20\Big) \\[1em] = ₹ \Big(\dfrac{100}{83} \times 448.20\Big) \\[1em] = ₹ 540$

Hence, the cost price is ₹ 540.

Find the cost price when:

S.P. = ₹ 1,479, Gain = $6\dfrac{1}{4}$%

Answer

Given:

S.P. = ₹ 1,479, Gain % = $6\dfrac{1}{4}$% = $\dfrac{25}{4}$%

$\text{C.P.} = \dfrac{100}{(100 + \text{gain percentage})} \times \text{S.P.} \\[1em] = ₹ \Big(\dfrac{100}{100 + \dfrac{25}{4}} \times 1479\Big) \\[1em] = ₹ \Big(\dfrac{100}{\dfrac{425}{4}} \times 1479\Big) \\[1em] = ₹ \Big(\dfrac{100 \times 4}{425} \times 1479\Big) \\[1em] = ₹ \Big(\dfrac{400}{425} \times 1479\Big) \\[1em] = ₹ 1392$

Hence, the cost price is ₹ 1,392.

Find the cost price when:

S.P. = ₹ 611.80, Loss = 8%

Answer

Given:

S.P. = ₹ 611.80, Loss % = 8%

$\text{C.P.} = \dfrac{100}{(100 - \text{loss percentage})} \times \text{S.P.} \\[1em] = ₹ \Big(\dfrac{100}{100 - 8} \times 611.80\Big) \\[1em] = ₹ \Big(\dfrac{100}{92} \times 611.80\Big) \\[1em] = ₹ 665$

Hence, the cost price is ₹ 665.

A sells a bicycle to B at a profit of 20% and B sells it to C at a profit of 5%. If C pays ₹ 3,780, what did A pay for it?

Answer

Given:

C pays ₹ 3,780 for the bicycle.

For B,

S.P. = ₹ 3,780 and Profit % = 5%.

$\text{C.P. of B} = \dfrac{100}{(100 + \text{profit percentage})} \times \text{S.P.} \\[1em] = ₹ \Big(\dfrac{100}{100 + 5} \times 3780\Big) \\[1em] = ₹ \Big(\dfrac{100}{105} \times 3780\Big) \\[1em] = ₹ 3600$

For A,

S.P. = ₹ 3,600 and Profit % = 20%.

$\text{C.P. of A} = \dfrac{100}{(100 + \text{profit percentage})} \times \text{S.P.} \\[1em] = ₹ \Big(\dfrac{100}{100 + 20} \times 3600\Big) \\[1em] = ₹ \Big(\dfrac{100}{120} \times 3600\Big) \\[1em] = ₹ 3000$

Hence, A paid ₹ 3,000 for the bicycle.

Raju sold a watch to Sonu at 12% gain and Sonu had to sell it to Manu at a loss of 5%. If Manu paid ₹ 5,320, how much did Raju pay for it?

Answer

Given:

Manu paid ₹ 5,320 for the watch.

For Sonu,

S.P. = ₹ 5,320 and Loss % = 5%.

$\text{C.P. of Sonu} = \dfrac{100}{(100 - \text{loss percentage})} \times \text{S.P.} \\[1em] = ₹ \Big(\dfrac{100}{100 - 5} \times 5320\Big) \\[1em] = ₹ \Big(\dfrac{100}{95} \times 5320\Big) \\[1em] = ₹ 5600$

For Raju, S.P. = ₹ 5,600 and Gain % = 12%.

$\text{C.P. of Raju} = \dfrac{100}{(100 + \text{gain percentage})} \times \text{S.P.} \\[1em] = ₹ \Big(\dfrac{100}{100 + 12} \times 5600\Big) \\[1em] = ₹ \Big(\dfrac{100}{112} \times 5600\Big) \\[1em] = ₹ 5000$

Hence, Raju paid ₹ 5,000 for the watch.

A grocer purchased 80 kg of rice at ₹ 27 per kg and mixed it with 120 kg of rice purchased at ₹ 32 per kg. At what rate per kg should he sell the mixture to gain 16%?

Answer

Given:

A grocer purchased 80 kg of rice at ₹ 27 per kg and 120 kg of rice at ₹ 32 per kg.

C.P. of 80 kg of rice = ₹ (80 × 27) = ₹ 2,160.

C.P. of 120 kg of rice = ₹ (120 × 32) = ₹ 3,840.

Total C.P. of the mixture = ₹ (2,160 + 3,840) = ₹ 6,000.

Total weight of the mixture = (80 + 120) kg = 200 kg.

Gain % = 16%.

$\text{S.P. of the mixture} = \dfrac{(100 + \text{gain percentage})}{100} \times \text{C.P.} \\[1em] = ₹ \Big(\dfrac{100 + 16}{100} \times 6000\Big) \\[1em] = ₹ \Big(\dfrac{116}{100} \times 6000\Big) \\[1em] = ₹ 6,960$

Selling price per kg = ₹ $\dfrac{6960}{200}$ = ₹ 34.80

Hence, he should sell the mixture at ₹ 34.80 per kg.

Mrs. Harjeet bought two bags for ₹ 1,150 each. She sold one of them at a gain of 6% and the other at a loss of 2%. How much did she gain?

Answer

Given:

C.P. of each bag = ₹ 1,150

For the first bag, Gain % = 6%.

Gain = 6% of ₹ 1,150 = ₹ $\Big(\dfrac{6}{100} \times 1150\Big)$ = ₹ 69.

For the second bag, Loss % = 2%.

Loss = 2% of ₹ 1,150 = ₹ $\Big(\dfrac{2}{100} \times 1150\Big)$ = ₹ 23.

Since the gain is more than the loss, there is a net gain.

Net gain = ₹ (69 - 23) = ₹ 46.

Hence, Mrs. Harjeet gained ₹ 46.

A trader purchased a wall clock and a watch for a sum of ₹ 5,070. He sold them making a profit of 10% on the wall clock and 15% on the watch. He earns a profit of ₹ 669.50. Find the cost price of the wall clock and that of the watch.

Answer

Let the cost price of the wall clock be ₹ $x$.

Then, the cost price of the watch = ₹ (5070 - $x$).

Profit on the wall clock = 10% of ₹ $x = ₹ \dfrac{10x}{100}$.

Profit on the watch = 15% of ₹ (5070 - $x$) = ₹ $\dfrac{15(5070 - x)}{100}$.

Total profit = ₹ 669.50.

$\Rightarrow \dfrac{10x}{100} + \dfrac{15(5070 - x)}{100} = 669.50 \\[1em] \Rightarrow 10x + 76050 - 15x = 66950 \\[1em] \Rightarrow -5x = 66950 - 76050 \\[1em] \Rightarrow -5x = -9100 \\[1em] \Rightarrow x = 1820$

C.P. of the wall clock = ₹ 1,820.

C.P. of the watch = ₹ (5,070 - 1,820) = ₹ 3,250.

Hence, the cost price of the wall clock is ₹ 1,820 and that of the watch is ₹ 3,250.

Toffees are bought at 15 for ₹ 20. How many toffees would be sold for ₹ 20 so as to gain 25%?

Answer

Given:

C.P. of 15 toffees = ₹ 20 and Gain % = 25%

$\text{S.P. of 15 toffees} = \dfrac{(100 + \text{gain percentage})}{100} \times \text{C.P.} \\[1em] = ₹ \Big(\dfrac{100 + 25}{100} \times 20\Big) \\[1em] = ₹ \Big(\dfrac{125}{100} \times 20\Big) \\[1em] = ₹ 25$

So, for ₹ 25 he sells 15 toffees.

⇒ For ₹ 20 he should sell $\Big(\dfrac{15}{25} \times 20\Big)$ = 12 toffees.

Hence, 12 toffees would be sold for ₹ 20 so as to gain 25%.

Two-thirds of a consignment was sold at a profit of 5% and the remainder at a loss of 2%. If the total profit was ₹ 4,000, find the value at which the consignment was purchased.

Answer

Let the cost price of the consignment be ₹ 100.

C.P. of $\dfrac{2}{3}$ of the consignment = ₹ $\dfrac{200}{3}$, sold at a profit of 5%.

Gain = ₹ $\Big(\dfrac{200}{3} \times \dfrac{5}{100}\Big) = ₹ \dfrac{10}{3}$.

C.P. of the remaining $\Big(1 - \dfrac{2}{3}\Big) = \dfrac{1}{3}$ of the consignment = ₹ $\dfrac{100}{3}$, sold at a loss of 2%.

Loss = ₹ $\Big(\dfrac{100}{3} \times \dfrac{2}{100}\Big) = ₹ \dfrac{2}{3}$.

Net profit = ₹ $\Big(\dfrac{10}{3} - \dfrac{2}{3}\Big) = ₹ \dfrac{8}{3}$.

If the profit is ₹ $\dfrac{8}{3}$, then C.P. = ₹ 100.

$\Rightarrow \text{If the profit is ₹ 4000, then C.P.} = ₹ \Big(100 \times \dfrac{3}{8} \times 4000\Big) \\[1em] = ₹ \dfrac{1200000}{8} \\[1em] = ₹ 150000$

Hence, the consignment was purchased for ₹ 1,50,000.

A grocer bought sugar worth of ₹ 4,500. He sold one-third of it at 10% gain. At what gain per cent, the remaining sugar be sold to have a 12% gain on the whole?

Answer

Given:

Total C.P. of the sugar = ₹ 4,500

C.P. of one-third of the sugar = ₹ $\Big(\dfrac{1}{3} \times 4500\Big)$ = ₹ 1,500, sold at a gain of 10%.

$\text{S.P. of this part} = ₹ \Big(\dfrac{100 + 10}{100} \times 1500\Big) \\[1em] = ₹ \Big(\dfrac{110}{100} \times 1500\Big) \\[1em] = ₹ 1650$

For a gain of 12% on the whole,

$\text{Total S.P.} = ₹ \Big(\dfrac{100 + 12}{100} \times 4500\Big) \\[1em] = ₹ \Big(\dfrac{112}{100} \times 4500\Big) \\[1em] = ₹ 5040$

S.P. of the remaining sugar = ₹ (5,040 - 1,650) = ₹ 3,390.

C.P. of the remaining sugar = ₹ (4,500 - 1,500) = ₹ 3,000.

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

Gain = ₹ (3,390 - 3,000) = ₹ 390.

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

= $\Big(\dfrac{390}{3000} \times 100\Big)$%

= $\dfrac{39000}{3000}$%

= 13%

Hence, the remaining sugar should be sold at a gain of 13%.

A man buys a piece of land for ₹ 3,84,000. He sells two-fifths of it at a loss of 6%. At what gain per cent should he sell the remaining piece of land to gain 10% on the whole?

Answer

Given:

Total C.P. of the land = ₹ 3,84,000

C.P. of two-fifths of the land = ₹ $\Big(\dfrac{2}{5} \times 384000\Big)$ = ₹ 1,53,600, sold at a loss of 6%.

$\text{S.P. of this part} = ₹ \Big(\dfrac{100 - 6}{100} \times 153600\Big) \\[1em] = ₹ \Big(\dfrac{94}{100} \times 153600\Big) \\[1em] = ₹ 144384$

For a gain of 10% on the whole,

$\text{Total S.P.} = ₹ \Big(\dfrac{100 + 10}{100} \times 384000\Big) \\[1em] = ₹ \Big(\dfrac{110}{100} \times 384000\Big) \\[1em] = ₹ 422400$

S.P. of the remaining land = ₹ (4,22,400 - 1,44,384) = ₹ 2,78,016.

C.P. of the remaining land = ₹ (3,84,000 - 1,53,600) = ₹ 2,30,400.

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

Gain = ₹ (2,78,016 - 2,30,400) = ₹ 47,616.

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

= $\Big(\dfrac{47616}{230400} \times 100\Big)$%

= $\dfrac{4761600}{230400}$%

= $\dfrac{62}{3}$%

= $20\dfrac{2}{3}$%

Hence, he should sell the remaining piece of land at a gain of $\mathbf{20\dfrac{2}{3}}$%.

By selling an almirah for ₹ 10,416, a man gains 12%. What will be his gain or loss per cent if it is sold for ₹ 9,114?

Answer

Given:

S.P. of the almirah = ₹ 10,416 and Gain % = 12%

$\text{C.P.} = \dfrac{100}{(100 + \text{gain percentage})} \times \text{S.P.} \\[1em] = ₹ \Big(\dfrac{100}{100 + 12} \times 10416\Big) \\[1em] = ₹ \Big(\dfrac{100}{112} \times 10416\Big) \\[1em] = ₹ 9300$

Now, the new S.P. = ₹ 9,114.

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

Loss = ₹ (9,300 - 9,114) = ₹ 186.

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

= $\Big(\dfrac{186}{9300} \times 100\Big)$%

= $\dfrac{18600}{9300}$%

= 2%

Hence, there will be a loss of 2%.

A chair was sold for ₹ 2,142 at a gain of 5%. At what price it should have been sold to gain 10%?

Answer

Given:

S.P. of the chair = ₹ 2,142 and Gain % = 5%

$\text{C.P.} = \dfrac{100}{(100 + \text{gain percentage})} \times \text{S.P.} \\[1em] = ₹ \Big(\dfrac{100}{100 + 5} \times 2142\Big) \\[1em] = ₹ \Big(\dfrac{100}{105} \times 2142\Big) \\[1em] = ₹ 2040$

Now, C.P. = ₹ 2,040 and the gain required = 10%.

$\text{Required S.P.} = \dfrac{(100 + \text{gain percentage})}{100} \times \text{C.P.} \\[1em] = ₹ \Big(\dfrac{100 + 10}{100} \times 2040\Big) \\[1em] = ₹ \Big(\dfrac{110}{100} \times 2040\Big) \\[1em] = ₹ 2244$

Hence, the chair should have been sold for ₹ 2,244 to gain 10%.

A television is sold for ₹ 9,360 at a loss of 4%. For how much it should have been sold to gain 4%?

Answer

Given:

S.P. of the television = ₹ 9,360 and Loss % = 4%

$\text{C.P.} = \dfrac{100}{(100 - \text{loss percentage})} \times \text{S.P.} \\[1em] = ₹ \Big(\dfrac{100}{100 - 4} \times 9360\Big) \\[1em] = ₹ \Big(\dfrac{100}{96} \times 9360\Big) \\[1em] = ₹ 9,750$

Now, C.P. = ₹ 9,750 and the gain required = 4%.

$\text{Required S.P.} = \dfrac{(100 + \text{gain percentage})}{100} \times \text{C.P.} \\[1em] = ₹ \Big(\dfrac{100 + 4}{100} \times 9750\Big) \\[1em] = ₹ \Big(\dfrac{104}{100} \times 9750\Big) \\[1em] = ₹ 10,140$

Hence, the television should have been sold for ₹ 10,140 to gain 4%.

A shopkeeper sold two fans at ₹ 1,980 each. On one he gained 10%, while on the other he lost 10%. Calculate the gain or loss per cent on the whole transaction.

Answer

Given:

S.P. of each fan = ₹ 1,980

For the first fan, S.P. = ₹ 1,980 and Gain % = 10%.

$\text{C.P.} = \dfrac{100}{(100 + \text{gain percentage})} \times \text{S.P.} \\[1em] = ₹ \Big(\dfrac{100}{110} \times 1980\Big) \\[1em] = ₹ 1800$

For the second fan, S.P. = ₹ 1,980 and Loss % = 10%.

$\text{C.P.} = \dfrac{100}{(100 - \text{loss percentage})} \times \text{S.P.} \\[1em] = ₹ \Big(\dfrac{100}{90} \times 1980\Big) \\[1em] = ₹ 2200$

Total C.P. of the two fans = ₹ (1,800 + 2,200) = ₹ 4,000.

Total S.P. of the two fans = ₹ (1,980 + 1,980) = ₹ 3,960.

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

Loss = ₹ (4,000 - 3,960) = ₹ 40.

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

= $\Big(\dfrac{40}{4000} \times 100\Big)$%

= 1%

Hence, there is a loss of 1% on the whole transaction.

Shanti sold two cameras for ₹ 6,555 each. On one she lost 5%, while on the other she gained 15%. Find the gain or loss per cent in the whole transaction.

Answer

Given:

S.P. of each camera = ₹ 6,555

For the first camera, S.P. = ₹ 6,555 and Loss % = 5%.

$\text{C.P.} = \dfrac{100}{(100 - \text{loss percentage})} \times \text{S.P.} \\[1em] = ₹ \Big(\dfrac{100}{95} \times 6555\Big) \\[1em] = ₹ 6900$

For the second camera, S.P. = ₹ 6,555 and Gain % = 15%.

$\text{C.P.} = \dfrac{100}{(100 + \text{gain percentage})} \times \text{S.P.} \\[1em] = ₹ \Big(\dfrac{100}{115} \times 6555\Big) \\[1em] = ₹ 5700$

Total C.P. of the two cameras = ₹ (6,900 + 5,700) = ₹ 12,600.

Total S.P. of the two cameras = ₹ (6,555 + 6,555) = ₹ 13,110.

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

Gain = ₹ (13,110 - 12,600) = ₹ 510.

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

= $\Big(\dfrac{510}{12600} \times 100\Big)$%

= $\dfrac{51000}{12600}$%

= $\dfrac{85}{21}$%

= $4\dfrac{1}{21}$%

Hence, there is a gain of $\mathbf{4\dfrac{1}{21}}$% in the whole transaction.

By selling 45 lemons for ₹ 40, a man loses 20%. How many should he sell for ₹ 24 to gain 20% on the transaction?

Answer

Given:

S.P. of 45 lemons = ₹ 40 and Loss % = 20%

$\text{C.P. of 45 lemons} = \dfrac{100}{(100 - \text{loss percentage})} \times \text{S.P.} \\[1em] = ₹ \Big(\dfrac{100}{80} \times 40\Big) \\[1em] = ₹ 50$

Now, the gain required = 20%.

$\text{S.P. of 45 lemons} = \dfrac{(100 + \text{gain percentage})}{100} \times \text{C.P.} \\[1em] = ₹ \Big(\dfrac{120}{100} \times 50\Big) \\[1em] = ₹ 60$

So, for ₹ 60 he sells 45 lemons.

⇒ For ₹ 24 he should sell $\Big(\dfrac{45}{60} \times 24\Big)$ = 18 lemons.

Hence, he should sell 18 lemons for ₹ 24 to gain 20%.

Rajni sold a pressure cooker at a loss of 8%. Had she bought it at 10% less and sold for ₹ 176 more, she would have gained 20%. Find the cost price of the pressure cooker.

Answer

Let the cost price of the pressure cooker be ₹ $x$.

When the loss is 8%, then S.P. = ₹ ($x$ - 8% of $x$) = ₹ $\dfrac{23x}{25}$.

New C.P. = ₹ ($x$ - 10% of $x$) = ₹ $\dfrac{9x}{10}$.

New S.P. = ₹ $\Big(\dfrac{23x}{25} + 176\Big)$.

On the new cost price, the gain is 20%.

$\Rightarrow \dfrac{23x}{25} + 176 = \dfrac{(100 + 20)}{100} \times \dfrac{9x}{10} \\[1em] \Rightarrow \dfrac{23x}{25} + 176 = \dfrac{120}{100} \times \dfrac{9x}{10} \\[1em] \Rightarrow \dfrac{23x}{25} + 176 = \dfrac{27x}{25} \\[1em] \Rightarrow \dfrac{27x}{25} - \dfrac{23x}{25} = 176 \\[1em] \Rightarrow \dfrac{4x}{25} = 176 \\[1em] \Rightarrow x = \dfrac{176 \times 25}{4} \\[1em] \Rightarrow x = 1100$

Hence, the cost price of the pressure cooker is ₹ 1,100.

A man sold a toaster at a profit of 10%. Had he purchased it for 5% less and sold it for ₹ 56 more, he could have gained 25%. For how much did he buy it?

Answer

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

When the profit is 10%, then S.P. = ₹ ($x$ + 10% of $x$) = ₹ $\dfrac{11x}{10}$.

New C.P. = ₹ ($x$ - 5% of $x$) = ₹ $\dfrac{19x}{20}$.

New S.P. = ₹ $\Big(\dfrac{11x}{10} + 56\Big)$.

On the new cost price, the gain is 25%.

$\Rightarrow \dfrac{11x}{10} + 56 = \dfrac{(100 + 25)}{100} \times \dfrac{19x}{20} \\[1em] \Rightarrow \dfrac{11x}{10} + 56 = \dfrac{125}{100} \times \dfrac{19x}{20} \\[1em] \Rightarrow \dfrac{11x}{10} + 56 = \dfrac{19x}{16} \\[1em] \Rightarrow \dfrac{19x}{16} - \dfrac{11x}{10} = 56 \\[1em] \Rightarrow \dfrac{95x - 88x}{80} = 56 \\[1em] \Rightarrow \dfrac{7x}{80} = 56 \\[1em] \Rightarrow x = \dfrac{56 \times 80}{7} \\[1em] \Rightarrow x = 640$

Hence, the man bought the toaster for ₹ 640.

A shopkeeper sells each of his goods at a gain of $22\dfrac{1}{2}$%. If on any day, his total sale was of ₹ 9,408, what was (i) the total cost of all the goods sold on that day (ii) his profit of that day.

Answer

Given:

Total S.P. of the goods = ₹ 9,408 and Gain % = $22\dfrac{1}{2}$% = $\dfrac{45}{2}$%

(i) Total cost of the goods:

$\text{C.P.} = \dfrac{100}{(100 + \text{gain percentage})} \times \text{S.P.} \\[1em] = ₹ \Big(\dfrac{100}{100 + \dfrac{45}{2}} \times 9408\Big) \\[1em] = ₹ \Big(\dfrac{100}{\dfrac{245}{2}} \times 9408\Big) \\[1em] = ₹ \Big(\dfrac{100 \times 2}{245} \times 9408\Big) \\[1em] = ₹ \Big(\dfrac{200}{245} \times 9408\Big) \\[1em] = ₹ 7680$

Hence, the total cost of all the goods sold on that day is ₹ 7,680.

(ii) Profit = S.P. - C.P. = ₹ (9,408 - 7,680) = ₹ 1,728.

Hence, his profit of that day is ₹ 1,728.