Class 8: Profit and Loss – Exercise 14B – ICSE / ISC / CBSE Mathematics Portal for K12 Students

Question 1: Find the selling price when:

$\displaystyle \text{i) } \text{C.P. } = \text{ Rs. } 7640 , \text{Gain } =15\%$ $\displaystyle \text{ii) } \text{C.P. } = \text{ Rs. } 4850 , \text{Loss } =12\%$

$\displaystyle \text{iii) } \text{C.P. } = \text{ Rs. } 720 , \text{Loss } = 8\frac{3}{4} \%$ $\displaystyle \text{iv) } \text{C.P. } = \text{ Rs. } 2652 , \text{Gain } = 16\frac{2}{3} \%$

Answer:

$\displaystyle \text{i) } \text{C.P. } = \text{ Rs. } 7640 , \text{Gain } =15\%$

$\displaystyle \text{S.P. } = \Big( 1+ \frac{15}{100} \Big) \times 7640=8786 \text{ Rs. }$

$\displaystyle \text{ii) } \text{C.P. } = \text{ Rs. } 4850 , \text{Loss } =12\%$

$\displaystyle \text{S.P. } = \Big( 1- \frac{12}{100} \Big) \times 4850=4268 \text{ Rs. }$

$\displaystyle \text{iii) } \text{C.P. } = \text{ Rs. } 720 , \text{Loss } = 8\frac{3}{4} \%$

$\displaystyle \text{S.P. } = \Big( 1- \frac{8\frac{3}{4}}{100} \Big) \times 720=657 \text{ Rs. }$

$\displaystyle \text{iv) } \text{C.P. } = \text{ Rs. } 2652 , \text{Gain } = 16\frac{2}{3}\%$

$\displaystyle \text{S.P. } = \Big( 1+ \frac{16\frac{2}{3}}{100} \Big) \times 2652=3094 \text{ Rs. }$

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Question 2: Find the Cost Price, When:

$\displaystyle \text{i) } \text{S.P. } = \text{ Rs. } 207 , \text{Gain } 15\%$ $\displaystyle \text{ii) } \text{S.P. } = \text{ Rs. } 448.20 , \text{Loss } 17\%$

$\displaystyle \text{iii) } \text{S.P. } = \text{ Rs. } 1479 , \text{Gain } 6 \%$ $\displaystyle \text{iv) } \text{S.P. } = \text{ Rs. } 611.80 , \text{Loss } 8\%$

Answer:

$\displaystyle \text{i) } \text{S.P. } = \text{ Rs. } 207 , \text{Gain } 15\%$

$\displaystyle \text{C.P. } = \Big( \frac{100}{100+15} \Big) \times 207=180 \text{ Rs. }$

$\displaystyle \text{ii) } \text{S.P. } = \text{ Rs. } 448.20 , \text{Loss } 17\%$

$\displaystyle \text{C.P. } = \Big( \frac{100}{100-17} \Big) \times 448.20=540 \text{ Rs. }$

$\displaystyle \text{iii) } \text{S.P. } = \text{ Rs. } 1479 , \text{Gain } 6 \%$

$\displaystyle \text{C.P. } = \Big( \frac{100}{100+6 \frac{1}{4}} \Big) \times 1479=1392 \text{ Rs. }$

$\displaystyle \text{iv) } \text{S.P. } = \text{ Rs. } 611.80 , \text{Loss } 8\%$

$\displaystyle \text{C.P. } = \Big( \frac{100}{100-8} \Big) \times 611.80=665 \text{ Rs. }$

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Question 3: A Sells a cycle to B at a Profit of $\displaystyle 20\%$ and B Sells it to C at a Profit of $\displaystyle 5\%$ . If C pays Rs. $\displaystyle 3780$ , What did A Pay for it?

Answer:

Let C.P. of A $\displaystyle = x$

Then, S.P. of A $\displaystyle =$ C.P. of B $\displaystyle = 1.2 x$

S.P. of B $\displaystyle = (1.2x) \times (1.05) =1.26x$

Therefore

$\displaystyle 1.26 x = 3780$

$\displaystyle x = 3000$

Hence A Paid Rs. $\displaystyle 3000$ for the cycle.

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Question 4: A Sold a watch to B at $\displaystyle 12\%$ gain and B had to sell if it Manu at a loss of $\displaystyle 5\%$ . If C Paid Rs. $\displaystyle 5320$ then how much did A Pay?

Answer:

Let C.P. of A $\displaystyle = x$

C.P. of B $\displaystyle =1.12x$

Then, S.P. of A $\displaystyle =$ C.P. of B $\displaystyle = 1.2 x$

S.P. of B $\displaystyle = (1.12x) \times (0.95) =1.064x$

Therefore

$\displaystyle 1.064 x = 5320$

$\displaystyle x = 5000$

Hence A Paid Rs. $\displaystyle 5000$ for the Watch

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Question 5: A Grocer Purchase $\displaystyle 80$ kg of Rice at Rs. $\displaystyle 27/Kg$ and mixed it with $\displaystyle 120$ kg of rice purchased at Rs. $\displaystyle 32/kg$ . At what rate per kg should he sell the mixture to $\displaystyle \text{Gain } 16\%$ ?

Answer:

$\displaystyle \text{Let Total } \text{C.P. } = 80 \times 27 + 120 \times 32 = 6000$

$\displaystyle \text{ For 16 \% gain Total S.P. } = \Big( \frac{100+16}{100} \Big) \times 6000=6960$

$\displaystyle \text{Total Quantity } = 80 + 120 = 200 kg$

$\displaystyle \text{Hence S.P. per kg } = \frac{6960}{200} =34.8 Rs. /kg$

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Question 6: A Bought two bags for Rs. $\displaystyle 1150$ each. A the sold one of them at a gain of $\displaystyle 6\%$ and the other at a loss of $\displaystyle 2\%$ . How much did A Gain?

Answer:

$\displaystyle \text{C.P. } \text{Total } = 1150 \times 2 = 2300 \text{ Rs. }$

$\displaystyle \text{ Total S.P. } = \Big( \frac{100+6}{100} \Big) \times 1150+ \Big( \frac{100-2}{100} \Big) \times 1150$

$\displaystyle = 1219 + 1127 = 2346 \text{ Rs. }$

$\displaystyle Gain \% = \Big( \frac{2346-2300}{2300} \Big) \times 100=2\%$

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Question 7: A trader purchased a wall clock and a watch for a sum of Rs. $\displaystyle 5070$ . He sold them making a profit of $\displaystyle 10\%$ on the wall clock and $\displaystyle 15\%$ on the watch he earns Rs. $\displaystyle 699.50$ . Find the cost price of the wall clock and that of the watch.

Answer:

$\displaystyle \text{Let the C.P. of wall clock } = {x}$

$\displaystyle \text{Let the C.P. of wall clock } = {y}$

Therefore

$\displaystyle \ {x + y} = 5070$

$\displaystyle \text{Also } 1.1{x} + 1.15{y} = 5070 + 669.5 \ = 5739.5$

$\displaystyle \text{Solving for } {x} \text{ and } {y}$ we get

$\displaystyle {x} =1820 \text{ Rs. or } {y} = 3250 \text{ Rs. }$

$\displaystyle \text{Hence Cost of Wall Clock } =1820 Rs.$ $\displaystyle \text{and Cost of Watch } = 3250 \text{ Rs. }$

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Question 8: Toffees are bought at $\displaystyle 15$ for Rs. $\displaystyle 20$ . How many toffees would be sold for Rs. $\displaystyle 20$ so as to $\displaystyle \text{Gain } 25\%$ ?

Answer:

$\displaystyle \text{C.P. of 15 Toffees } = 20 \text{ Rs. }$

$\displaystyle \text{Therefore, C.P. of 1 Toffee } = \frac{20}{15} \text{ Rs. }$

$\displaystyle \text{For } 25\% \text{ gain, S.P. of 1 Toffee} = \frac{20}{15} \times 1.25 = \frac{25}{15} \text{ Rs. }$

$\displaystyle \text{Therefore no. of toffees you can sell in 20 Rs. } = \frac{20}{25/15} = \frac{20 \times 15}{25} =12$

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Question 9: Two-thirds of a consignment was sold at a profit of $\displaystyle 5\%$ and the remaining at a loss of $\displaystyle 2\%$ . If the total profit was Rs. $\displaystyle 4000$ , Find the value at which the consignment was purchase?

Answer:

Let the C.P. of Consignment $\displaystyle = \textit{x}$

Therefore

$\displaystyle \frac{2}{3} x \times 1.05+ \frac{1}{3} x \times 0.98=x+4000$

$\displaystyle \frac{70}{100} x+ \frac{98}{300} x=x+4000$

$\displaystyle \frac{8}{300} x=4000 \ or \ x=150000 Rs$

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Question 10: A Grocer bought sugar worth Rs. $\displaystyle 4500$ . He sold $\displaystyle 1/3$ of it at $\displaystyle 10\%$ Gain. At what $\displaystyle \text{Gain } \%$ the remaining sugar be sold to have a $\displaystyle 12\%$ gain on the whole?

Answer:

C.P. of sugar $\displaystyle = 4500 \text{ Rs. }$

$\displaystyle \text{ Let the Gain \% of on the remaining sugar } = \text{x }\%$

Therefore

$\displaystyle \frac{1}{3} \times 4500 \times 1.1+ \frac{2}{3} \times 4500 \times \ \Big( 1+ \frac{x}{100} \Big) =4500 \times 1.12$

$\displaystyle 1650+3000+30x=5040 \ or \ x=13\%$

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Question 11: A Man buys a piece of land for Rs. $\displaystyle 38400$ . He sells $\displaystyle 2/5$ of at a loss of $\displaystyle 6\%$ . At what $\displaystyle \text{Gain } \%$ , the remaining piece of land be sold to $\displaystyle \text{Gain } 10\%$ on the whole?

Answer:

C.P. of land $\displaystyle = 38400 \text{ Rs. }$

$\displaystyle \frac{2}{5}$ the of land sold at a loss of $\displaystyle 6\%$

Let’s the remainder be sold at $\displaystyle x \%$ gain

Therefore

$\displaystyle \frac{2}{5} \times 38400 \times 0.94+ \frac{3}{5} \times 38400\ \times \Big( 1+ \frac{x}{100} \Big) =38400 \times 1.1$

$\displaystyle 14438.4+23040(1+0.01x)=42240$

$\displaystyle \text{Solving for } x \text{ we get } x =20 \frac{2}{3} \%$

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Question 12: By Selling a car for Rs. $\displaystyle 10416$ , a man $\displaystyle \text{Gain } 12\%$ . What will be his gain or loss percent if it is sold for Rs. $\displaystyle 9114$ .

Answer:

Let the cost of the car $\displaystyle = x$

Therefore,

$\displaystyle \Big( 1+ \frac{12}{100} \Big) x=10416 \ or \ x=9300 \text{ Rs. }$

$\displaystyle x = 9300 \text{ Rs. }$

If S.P $\displaystyle = Rs. 9114$

$\displaystyle Loss \%= \Big( \frac{9300-9114}{9300} \Big) \times 100=2\%$

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Question 13: A Chair sold for Rs. $\displaystyle 2142$ at a Gain at $\displaystyle 5\%$ At what price should it be sold to $\displaystyle \text{Gain } 10\%$

Answer:

Let The C.P. of chair $\displaystyle = {x}$

Then, $\displaystyle \Big( 1+ \frac{5}{100} \Big) x=2142 or x=2040 \text{ Rs. }$

For $\displaystyle 10\%$ Gain

$\displaystyle \text{S.P. } = \Big( 1+ \frac{10}{100} \Big) \times 2040=2244 \text{ Rs. }$

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Question 14: A television is sold for Rs. $\displaystyle 9360$ at a loss of $\displaystyle 4\%$ . For how much it should have been sold be $\displaystyle \text{Gain } 4\%$ ?

Answer:

Let the C.P. of Television $\displaystyle = {x}$

$\displaystyle \Big( 1- \frac{4}{100} \Big) x=9360 \text{ or } x=9750 Rs$

$\displaystyle \text{To Gain } 4\%,$

$\displaystyle \text{S.P. } = \Big( 1+ \frac{4}{100} \Big) \times 9750=10140 \text{ Rs. }$

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Question 15: A shop keeper sold two fans at Rs. $\displaystyle 1980$ each. On one he gained $\displaystyle 10\%$ , while other he cost $\displaystyle 10\%$ . Calculate the gain or loan percent on whole transaction?

Answer:

Let C.P. of $\displaystyle 1^{st}$ fan $\displaystyle = {x} \text{ Rs. }$

Let C.P. of $\displaystyle 2^{nd}$ fan $\displaystyle = {y} \text{ Rs. }$

Therefore, $\displaystyle \Big( 1+ \frac{10}{100} \Big) x=1980 \text{ or } x=1800$

Similarly $\displaystyle \Big( 1- \frac{10}{100} \Big) y=1980 \text{ or } y=2200$

Hence, Total $\displaystyle \text{C.P. } = 1800 + 2200 = 4000 \text{ Rs. }$

Total $\displaystyle \text{S.P. } = 2 \times 1980 = 3960 \text{ Rs. }$

$\displaystyle \text{Loss } \%= \Big( \frac{4000-3960}{4000} \Big) \times 100=1\%$

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Question 16: Shanti sold two cameras for Rs. $\displaystyle 6555$ each. On one she lost $\displaystyle 5\%$ , while on the other she gained $\displaystyle 15\%$ . Find the gain or loss percentage in whole transaction.

Answer:

Let, C.P. of $\displaystyle 1^{st}$ Camera $\displaystyle = {x}$

Let C.P. of $\displaystyle 2^{nd}$ Camera $\displaystyle = {y}$

Therefore, $\displaystyle \Big( 1- \frac{5}{100} \Big) x=6555 \text{ or }x=6900$

Similarly $\displaystyle \Big( 1+ \frac{15}{100} \Big) y=6555 \text{ or } y=5700$

Total $\displaystyle \text{C.P. } = 6900 + 5700 = 12600 \text{ Rs. }$

Total $\displaystyle \text{S.P. } = 2 \times 6555 = 13110 \text{ Rs. }$

$\displaystyle Gain \%= \Big( \frac{13110-12600}{12600} \Big) \times 100=4 \frac{1}{21} \%$

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Question 17: By selling $\displaystyle 45$ lemons for Rs. $\displaystyle 40$ , a man loses $\displaystyle 20\%$ how many should he sell for Rs. $\displaystyle 24$ to $\displaystyle \text{Gain } 20\%$ on the transaction.

Answer:

$\displaystyle \text{Let C.P. of a lemon } = x \text{ Rs. }$

$\displaystyle \text{S.P. of one Lemon } = \frac{40}{45} \text{ Rs. }$

$\displaystyle \text{ Therefore } \Big( 1- \frac{20}{100} \Big) x= \frac{40}{50} \ or \ x= \frac{10}{9} \text{ Rs. }$

$\displaystyle \text{To } \text{Gain } 20\%$ on the transaction,

$\displaystyle \text{S.P. of one Lemon } = \Big( 1+ \frac{20}{100} \Big) \times \frac{10}{9} =\ \frac{4}{3} \text{ Rs. }$

$\displaystyle \text{Need to be sold for } 24 \text{ Rs. } = \frac{24}{4/3} =18 \text{ Lemons }$

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Question 18: A sold a pressure cooker at a loss of $\displaystyle 8\%$ . Had she bought it at $\displaystyle 10\%$ less and sold for Rs. $\displaystyle 176$ more, she would have gained $\displaystyle 20\%$ . Find the cost price of the pressure cooker.

Answer:

Let the cost of pressure cooker $\displaystyle = x$

$\displaystyle \text{S.P. } = 0.92x$

New $\displaystyle \text{C.P. } = 0.9x$

New $\displaystyle \text{S.P. } = 0.92x + 176$

$\displaystyle \text{ Therefore Gain } \%$

$\displaystyle \frac{0.92x+176-0.9x}{0.9x} = \frac{20}{100}$

$\displaystyle \frac{0.2x+176}{0.9x} = \frac{20}{100}$

$\displaystyle 2x+17600=8x \text{ or } x=1100 \text{ Rs. }$

Cost of the cooker $\displaystyle = 1100 \text{ Rs. }$

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Question 19: A Man sold a toaster at a profit of $\displaystyle 10\%$ . Had he purchased of for $\displaystyle 5\%$ less and sold it for $\displaystyle 56 \text{ Rs. }$ more, he would have gained $\displaystyle 25\%$ . How much did he buy for?