3 Mark Question

Question 13 Marks

On selling a bat for Rs. 486 a man loses 10%. Find the cost price of the bat.

Answer

SP of the bat = Rs. 486
Loss = 10%
CP of the bat
$=\Big\{\frac{100}{(100-\text{Loss%)}}\times\text{SP}\Big\}$
$=\Big\{\frac{100}{(100-10)}\times486\Big\}$
$=\frac{48600}{90}$
$=\text{Rs. }540$
CP of the bat = Rs. 540

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Question 23 Marks

Find the C.P. when:
S.P. = Rs. 1755, gain $=12\frac{1}{2}\%$

Answer

S.P. = Rs. 1755Gain% $=12\frac{1}{2}\%$
$=\frac{25}{2}\%$ $\therefore\text{C.P.}=\frac{\text{S.P.}\times100}{100+\text{gain%}}$ $=\frac{1755\times100}{100+\frac{25}{2}}$ $=\text{Rs. }\frac{1755\times100}{\frac{200+25}{2}}$ $=\frac{1755\times100\times2}{225}$ $=\text{Rs. }\frac{195\times4\times2}{1}$ $=\text{Rs. }1560$

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Question 33 Marks

Sudhir bought an almirah for Rs. 13600 and spent Rs. 400 on its transportation. He sold it for Rs. 16800. Find his gain percent.

Answer

C.P. of an almirah = Rs. 13600Amount spent on transportation = Rs. 400
Total cost price (CP) = Rs. 13600 + Rs. 400 = Rs. 14000
SP = Rs. 16800
Total gain = SP - CP
= Rs. 16800 - Rs. 14000 = Rs. 2800
$\therefore\text{Gain%}=\frac{\text{Total gain}\times100}{\text{CP}}$
$=\frac{2800\times100}{14000}$
$=20\%$

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Question 43 Marks

If the selling price of 10 pens is equal to the cost price of 14 pens, find gain percent.

Answer

Let the cost of each pen be Rs. 1
CP of 10 pens = Rs. 10
SP of 10 pens = CP of 14 pens = Rs. 14
Gain = SP - CP = 14 - 10 = Rs. 4
$\text{Gain}\%=\Big(\frac{\text{Gain}}{\text{CP}}\times100\Big)\%$
$=\Big(\frac{4}{10}\times100\Big)\%$
$=40\%$

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Question 53 Marks

Find the SP when:
C.P. = Rs. 950, gain = 6%

Answer

C.P. = Rs. 950
Gain% = 6%
$\therefore\text{S.P.}=\frac{\text{C.P}\times(100+\text{gain%})}{100}$
$=\frac{950(100+6)}{100}$
$=\frac{950\times106}{100}$
$=\text{Rs. }1007$

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Question 63 Marks

Find the C.P. when:
SP = Rs. 5600, loss $=6\frac{2}{3}\%$

Answer

S.P. = Rs. 5600 Loss $=6\frac{2}{3}\%$$=\frac{20}{3}\%$
$\therefore\text{C.P.}=\frac{\text{S.P.}\times100}{100-\text{Loss%}}$ $=\text{Rs. }\frac{5600\times100}{100-\frac{20}{3}}$ $=\text{Rs. }\frac{5600\times100\times3}{280}$ $=\text{Rs. }6000$

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Question 73 Marks

Ravi purchased an old house for Rs. 765000 and spent Rs. 115000 on its repairs, then, he sold it at a gain of 5%. How much did he get?

Answer

CP of an old house = Rs. 765000
Amount spent on repairs = Rs. 115000
Total cost price (CP) = Rs. 765000 + Rs. 115000 = Rs. 880000
Gain = 5%
$\therefore\text{SP of the house}=\frac{\text{C.P}\times(100+\text{gain%})}{100}$
$=\frac{880000\times(100+5)}{14000}$
$=\text{Rs. }\frac{880000\times105}{100}$
$=\text{Rs. }924000$

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Question 83 Marks

On selling an exhaust fan for Rs. 7350, a man gains $\frac{1}{6}$ of its cost price. Find the cost price of the fan.

Answer

SP of an exhaust fan = Rs. 7350
Gain $=\frac{1}{6}$ of CP
Then gain $=\frac{1}{6}$ of $\text{x}=\text{Rs. }\frac{\text{x}}{6}$
$\therefore\text{SP}=\text{x}+\frac{\text{x}}{6}$
$=\frac{7\text{x}}{6}$
Now $\frac{7\text{x}}{6}=7350$
$\Rightarrow\text{x}=\frac{7350\times6}{7}$
$=\text{Rs. }1050\times6$
$=\text{Rs. }6300$
Cost price of the fan = Rs. 6300

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Question 93 Marks

Find the SP when:
C.P. = Rs. 9600, gain $=16\frac{2}{3}\%$

Answer

C.P. = Rs. 9600
Gain% $=16\frac{2}{3}\%$
$\therefore\text{S.P.}=\frac{\text{C.P}\times(100+\text{gain%})}{100}$
$=\frac{950\Big(100+\frac{50}{3}\Big)}{100}$
$=\frac{9600\times350}{100\times3}$
$=\text{Rs. }11200$

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Question 103 Marks

The selling price of 12 pens is equal to the cost price of 15 pens. Find the gain percent.

Answer

Let the cost price of the pen be Re 1.
Cost price of 12 pens = Rs. 12
SP of 12 pens = CP of 15 pens = Rs. 15
Gain = SP - CP = Rs. (15 - 12) = Rs. 3
$\therefore\text{Gain}\%=\Big(\frac{\text{Gain}}{\text{CP}}\times100\Big)\%$
$=\Big(\frac{3}{12}\times100\Big)\%$
$=25\%$
Gain% = 25%

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Question 113 Marks

Find the C.P. when:
S.P. = Rs. 924, gain = 10%

Answer

S.P. = Rs. 924
Gain% = 10%
$\therefore\text{C.P.}=\frac{\text{S.P.}\times100}{100+\text{gain%}}$
$=\text{Rs. }\frac{924\times100}{100+10}$
$=\text{Rs. }\frac{924\times100}{110}$
$=\text{Rs. }840$

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Question 123 Marks

By selling a chair for Rs. 1375 a man gains 10%. Find its cost price.

Answer

SP of the chair = Rs. 1375
Gain% = 10
CP of the chair
$=\Big\{\frac{100}{(100+\text{Gsin%})}\times\text{SP}\Big\}$
$=\Big\{\frac{100}{(100+10)}\times1375\Big\}$
$=\frac{137500}{110}$
$\text{Rs. }1250$

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Question 133 Marks

On selling a watch for Rs. 11400, a shopkeeper loses 5%. For how much did he purchase it?

Answer

SP of a watch = Rs. 11400
Loss = 5%
$\text{CP of a watch}=\frac{\text{SP}\times100}{100-\text{loss%}}$
$=\frac{11400\times100}{100-5}$
$=\text{Rs. }\frac{11400\times100}{95}$
$=\text{Rs. }12000$

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Question 143 Marks

Find the gain or loss per cent when:
CP = Rs. 1650 and SP = Rs. 1452

Answer

C.P. = Rs. 1650
SP = Rs. 1452
Gain = CP - SP
= Rs. 1650 - Rs. 1452 = Rs. 198
$\therefore\text{Loss%}=\frac{\text{Total Loss}\times100}{\text{CP}}$
$=\frac{198\times100}{1650}$
$=12\%$

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Question 153 Marks

Mohit sold a watch to Karim at a gain of 10% and Karim sold it to Rahim at a gain of 4%. If Rahim pays Rs. 14300 for it, for how much did Mohit purchase it?

Answer

Let CP of watch for Mohit = Rs. 100
Gain =10%
SP for Mohit = Rs. 100 + 10 = Rs. 110
CP for Karim = Rs. 110
Gain = 4%
SP for karim,
$=\text{Rs. }\frac{110\times(100+4)}{100}$
$=\text{Rs. }\frac{110\times104}{100}$
$=\text{Rs. }\frac{1144}{10}$
Or CP for Rahime is Rs. $\frac{1144}{10},$ the CP
For Mohit = Rs. 100
And if CP for Rahim is Rs. 14300, then
CP Mohit $= \text{Rs. }\frac{100\times14300\times10}{1144}$
$=\text{Rs. }12500$

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Question 163 Marks

A vendor buys lemons at Rs. 25 per dozen and sells them at the rate of 5 for Rs. 12. Find his gain or loss percent.

Answer

CP of 1 dozen or 12 lemons = Rs. 25
SP of 5 lemons = Rs. 12
$\therefore\text{SP of 12 lemons}=\text{Rs. }\frac{12\times12}{5}$
$=\text{Rs. }\frac{144}{5}$
$=\text{Rs. }28.80$
Gain = SP - CP
Rs. 28.80 - Rs. 25 = Rs. 3.80
$\therefore\text{Gain}\%=\frac{\text{Total gain}\times100}{\text{CP}}$
$=\frac{3.80\times100}{25}=15.2\%$
$=15.2\%$

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Question 173 Marks

Find the SP when:
CP = Rs. 1540, loss = 4%

Answer

C.P. = Rs. 1540
Loss = 4%
$\therefore\text{S.P.}=\frac{\text{C.P}\times(100-\text{Loss%})}{100}$
$=\frac{1540\times(100-4)}{100}$
$=\frac{1540\times96}{100}$
$=\text{Rs. }1478.40$

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Question 183 Marks

Find the C.P. when:
SP = Rs. 8510, loss = 8%

Answer

S.P. = Rs. 8510Gain% 8%
$\therefore\text{C.P.}=\frac{\text{S.P.}\times100}{100-\text{Loss%}}$ $=\frac{8510\times100}{100-8}$ $=\text{Rs. }\frac{8510\times100}{92}$ $=\text{Rs. }9250$

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Question 193 Marks

Find the gain or loss per cent when:
CP = Rs. 1800 and SP = Rs. 1611

Answer

C.P. = Rs. 1800
SP = Rs. 1611
$\therefore$ Loss = SP - CP
= 1800 - 1611
= Rs. 189
$\therefore\text{Loss%}=\frac{\text{Total Loss}\times100}{\text{CP}}$
$=\frac{189\times100}{1800}$
$=\frac{21}{2}\%$
$=10.5\%$

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Question 203 Marks

Manoj purchased a video for Rs. 12000. He sold it to Rahul at a gain of 10%. If Rahul sells it to Rakesh at a loss of 5%, what did Rakesh pay for it?

Answer

For Manoj
CP of video = Rs. 12000
Gain = 10%
$\therefore\text{SP of video}\%=\frac{\text{CP}\times(100+\text{gain%})}{100}$
$=\frac{12000\times(100+10)}{100}$
$=\text{Rs. }\frac{12000\times110}{100}$
$=\text{Rs. }13200$
Or CP for Rahul = Rs. 13200
Loss = 5%
$\therefore\text{SP for Rahul}= \frac{13200\times(100-5)}{100}$
$=\text{Rs. }\frac{13200\times95}{100}$
$\text{Rs. }12540$
$\therefore$ CP for Rakesh = Rs. 12540

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Question 213 Marks

The selling price of 16 spoons is equal to the cost price of 15 spoons. Find the loss percent.

Answer

Let the cost price of one spoon be Re 1.
CP of 16 spoons = Rs. 16
SP of 16 spoons = CP of 15 spoons = Rs. 15
Loss = CP - SP = (16 - 15) = Re 1
$\text{Loss}\%=\Big(\frac{\text{Loss}}{\text{CP}}\times100\Big)\%$
$=\Big(\frac{31}{16}\times100\Big)\%$
$=6.25\%$
Loss% = 6.25%

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Question 223 Marks

Find the SP when:
CP = Rs. 8640, loss $=12\frac{1}{2}\%$

Answer

C.P. = Rs. 8640
Loss $=12\frac{1}{2}=\frac{25}{2}\%5$
$\therefore\text{S.P.}=\frac{\text{C.P}\times(100-\text{Loss%})}{100}$
$=\text{Rs. }\frac{8640\times\Big(100-\frac{25}{2}\Big)}{100}$
$=\text{Rs. }\frac{8640\times175}{2\times100}$
$=\text{Rs. }7560$

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Question 233 Marks

Find the gain or loss per cent when:
CP = Rs. 2400 and SP = Rs. 2592

Answer

C.P. = Rs. 2400
SP = Rs. 2592
Gain = SP - CP
= Rs. 2592 - Rs. 2400 = Rs. 192
$\therefore\text{Gain%}=\frac{\text{Total gain}\times100}{\text{CP}}$
$=\frac{192\times100}{2400}$
$=8\%$

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Question 243 Marks

If the manufacturer gains 10% the wholesale dealer 15%, and the retailer 25% then what is the productions cost of a washing machine whose retail price is Rs. 37950?

Answer

Retail price or S.P. of the machine for retailer = Rs. 37950
Gain = 25%
$\therefore\text{CP for retailer}=\frac{\text{S.P.}\times100}{100+\text{gain}}$
$=\text{Rs. }\frac{37950\times100}{100+25}$
$=\text{Rs. }\frac{37950\times100}{125}$
$=\text{Rs. }30360$
Or S.P. for wholesalar = Rs. 30360
Gain 15%
$\therefore$ C.P. for wholesalar $=\text{Rs. }\frac{30360\times100}{100+15}$
$=\text{Rs. }\frac{30360\times100}{115}$
$=\text{Rs. }26400$
Or S.P. for manufacturer = Rs. 26400
Gain = 10%
$\therefore$ C.P. for production $=\text{Rs. }\frac{26400\times100}{100 + 10}$
$=\text{Rs. }\frac{26400\times100}{110}$
$=\text{Rs. }24000$

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Question 253 Marks

Find the gain or loss per cent when:
CP = Rs. 12000 and SP = Rs. 12800

Answer

C.P. = Rs. 12000
SP = Rs. 12800
Gain = SP - CP
= Rs. 12800 - Rs. 12000 = Rs. 800
$\therefore\text{Gain%}=\frac{\text{Total gain}\times100}{\text{CP}}$
$=\frac{800\times100}{12000}$
$=\frac{20}{3}\%$
$=6\frac{2}{3}\%$

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Question 263 Marks

On selling a fan for Rs. 2585 a man gains $\frac{1}{2}$ of its cost price. Find the cost price of the fan.

Answer

Let the cost price of the fan be Rs. x.
$\text{Gain}=\text{Rs. }\frac{\text{x}}{10}$
SP of the fan $=\Big(\text{x}+\frac{\text{x}}{10}\Big)$
$=\text{Rs. }\frac{11}{10}\text{x}$
SP of the fan = Rs. 2585
$\therefore\frac{11}{10}\text{x}=2585$
$\Rightarrow11\text{x}=25850$
$\Rightarrow\text{x}=\frac{25850}{11}=2350$
So, CP of the fan is Rs. 2350.

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