Question 1: Find the selling price when:

i) C.P. = Rs. 7640 Gain =15\%            ii) C.P. = Rs. 4850 , Loss =12\%

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

Answer:

i)  C.P. = Rs. 7640 Gain =15\%

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

ii)  C.P. = Rs. 4850 , Loss =12\%

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

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

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

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

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

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Question 2: Find the Cost Price, When:

i) S.P. = Rs. 207 , Gain 15\%          ii) S.P. = Rs. 448.20 , Loss 17\%

iii) S.P. = Rs. 1479 , Gain 6 \%          iv) S.P. = Rs. 611.80 , Loss 8\%

Answer:

i)  S.P. = Rs. 207 , Gain 15\%

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

ii)  S.P. = Rs. 448.20 , Loss 17\%

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

iii)  S.P. = Rs. 1479 , Gain 6 \%

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

iv)  S.P. = Rs. 611.80 , Loss 8\%

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

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

Answer:

Let C.P. of A = x

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

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

Therefore

 1.26 x = 3780

 x = 3000

Hence A Paid Rs. 3000 for the cycle.

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

Answer:

Let C.P. of A = x

C.P. of B =1.12x

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

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

Therefore

 1.064 x = 5320

 x = 5000

Hence A Paid Rs. 5000 for the Watch

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

Answer:

Let Total C.P. = 80 \times 27 + 120 \times 32 = 6000

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

Total Quantity = 80 + 120 = 200 kg

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

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

Answer:

Total C.P. = 1150 \times 2 = 2300 Rs.

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

 = 1219 + 1127 = 2346 Rs.

 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. 5070 . He sold them making a profit of 10\% on the wall clock and 15\% on the watch he earns Rs. 699.50 . Find the cost price of the wall clock and that of the watch.

Answer:

Let the C.P. of wall clock = {x}

Let the C.P. of wall clock = {y}

Therefore

 \ {x + y} = 5070

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

Solving for {x} \ and \ {y} we get

 {x} =1820 Rs. \ or \ {y} = 3250 Rs.

Hence Cost of Wall Clock =1820 Rs. and Cost of Watch = 3250 Rs.

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Question 8: Toffees are bought at 15 for Rs. 20 . How many toffees would be sold for Rs. 20 so as to gain 25\% ?

Answer:

C.P. of 15 Toffees = Rs. 20

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

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

Therefore number of toffees that you can sell in 20 Rs = \frac{20}{25/15} = \frac{20 \times 15}{25} =12 Toffees

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

Answer:

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

Therefore

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

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

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

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

Answer:

C.P. of sugar = 4500 Rs.

Let the Gain \% of on the remaining sugar = \textit{x }\%

Therefore

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

 1650+3000+30x=5040 \ or \  x=13\%

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

Answer:

C.P. of land = 38400 Rs.

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

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

Therefore

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

14438.4+23040(1+0.01x)=42240

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

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

Answer:

Let the cost of the car = x

Therefore,

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

 x = 9300 Rs.

If S.P = Rs. 9114

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

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

Answer:

Let The C.P. of chair = {x}

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

For 10\% Gain

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

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Question 14: A television is sold for Rs. 9360 at a loss of 4\% . For how much it should have been sold be gain 4\% ?

Answer:

Let the C.P. of Television = {x}

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

To gain 4\%,

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

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

Answer:

Let C.P. of 1^{st} fan = {x} Rs.

Let C.P. of 2^{nd} fan = {y} Rs.

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

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

Hence, Total C.P. = 1800 + 2200 = 4000 Rs.

Total S.P. = 2 \times 1980 = 3960 Rs.

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

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

Answer:

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

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

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

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

Total C.P. = 6900 + 5700 = 12600 Rs.

Total S.P. = 2 \times 6555 = 13110 Rs.

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

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

Answer:

Let C.P. of a lemon = x Rs.

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

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

To gain 20\% on the transaction,

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

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

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

Answer:

Let the cost of pressure cooker = x

S.P. = 0.92x

New C.P. = 0.9x

New S.P. = 0.92x + 176

Therefore Gain \%

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

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

 2x+17600=8x \ or \  x=1100 Rs.

Cost of the cooker = 1100 Rs.

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

Answer:

Let, C.P. of Toaster = x

S.P. of Toaster = 1.1x

New C.P. = 0.95x

New S.P. =1.1x + 56

Gain = 25\%

Therefore: \frac{1.1x+56-0.95x}{0.95x} = \frac{25}{100}

 \frac{0.15x+56}{0.95x} = \frac{25}{100}

 15x+5600=23.75x \ or \  x=640 Rs.

The man bought the toaster for Rs. 640

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Question 20: A shopkeeper sells each of his goods at a gain of . If on any day, his total sell was Rs. 9408 , what was?

i) The total cost of all goods sold on that day          ii) His profit of that day

Answer:

Let the total C.P. of goods = x

Therefore,

 \Big( 1+ \frac{22.5}{100} \Big) x=9408 or x=7680 Rs.

Profit for day = 9408-7680 =1728 Rs.