5 Marks Questions

Question 15 Marks

A man buys lemons at $6$ for $Rs. 10$ and sells at 8 for $Rs. 15$ Find his gain percent.

Answer

Cost price of six lemons $= Rs. 10$
Cost price of one lemon $=\text{Rs. }\frac{10}{6}$
Cost price of eight lemons $=8\times\frac{10}{6}$
$=\text{Rs. }\frac{80}{6}$
$=\text{Rs. }13.33$ Selling price of eight lemons $= Rs. 15$
Gain $= SP - CP = Rs. (15 - 13.33) = Rs. 1.67$
$\text{Gain%}=\Big(\frac{\text{Gain}}{\text{C.P.}}\times100\Big)\%$
$=\Big(\frac{1.67}{13.33}\times100\Big)\%$$=12.5\%$

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Question 25 Marks

Mr Mehta purchased a video for $Rs. 20000$ and a television for $Rs. 30000.$ On the video he lost $5\%$ and on the television he gained $8\%$. Find his total gain or loss percent.

Answer

CP of video $= Rs. 20000$ And $CP$ of
television $= Rs. 30000$
Loss on video $= 5\%$ And gain on $TV = 8\%$
$\therefore\text{SP of video}\%=\frac{\text{CP}\times(100-\text{loss%})}{100}$
$=\text{Rs. }\frac{20000\times(100-5)}{100}$
$=\text{Rs. }\frac{20000\times95}{100}$
$=\text{Rs. }19000$ And $SP$ of $TV$
$= \text{Rs. }\frac{30000\times(100+8)}{100}$
$=\text{Rs. }\frac{30000\times108}{100}$
$=\text{Rs. }32400$
Total CP of video and $TV, = Rs. 20000 + 30000 = Rs. 50000$ And
SP of video and $TV, = Rs. 190000 + 32400 = RS. 51400$
Gain $= SP - CP = Rs. 51400 - 50000 = Rs. 1400$
$\therefore\text{Gain%}=\frac{\text{Gain}\times100}{\text{CP}}$
$=\frac{1400\times100}{50000}=\frac{14\%}{5}$
$=2\frac{4}{5}=2.8\%$

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Question 35 Marks

On selling a computer for $Rs. 24480,$ a dealer loses $4\%$. For how much should he sell it to gain $4\%?$

Answer

SP of a computer $= Rs. 24480$
Loss $= 4\%$
$\therefore\text{CP}=\frac{\text{SP}\times100}{100-\text{loss%}}$
$=\text{Rs.}\frac{24480\times100}{100-4}$
$=\text{Rs. }\frac{24480\times100}{96}$
$=\text{Rs. }25500$ In second case, gain $= 4\%$
$\therefore SP$ of the computer, $=\frac{\text{CP}\times(100+\text{gain}\%)}{100}$
$=\text{Rs. }\frac{25500\times(100+4)}{100}$
$=\text{Rs. }\frac{25500\times104}{100}$
$=\text{Rs. }26520$

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Question 45 Marks

On selling a calculator for $Rs. 1325$, a man gains $6\%$. For how much should he sell it to gain $12\%?$

Answer

$SP$ of a calculator $= Rs. 1325$ Gain $= 6\%$
$\text{CP}=\frac{\text{SP}\times100}{100+\text{gain%}}$
$=\frac{1325\times100}{100+6}$
$=\text{Rs. }\frac{1325\times100}{106}$
$=\text{Rs. }1250$ In second case, gain $= 12\%$
$\therefore SP$ of the calculator, $=\frac{\text{CP}\times(100+\text{gain}\%)}{100}$
$=\text{Rs. }\frac{1250\times(100+12)}{100}$
$=\text{Rs. }\frac{1250\times112}{100}$
$=\text{Rs. }1400$

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Question 55 Marks

A tricycle is sold at a gain of $15\%$. Had it been sold for $Rs. 108$ more, the profit would have been $20\%$. Find its cost price.

Answer

Let the $CP$ of the tricycle be $Rs. x$
$\text{SP at 15% gain}=\Big\{\frac{(100+\text{Gain%})}{100}\times\text{CP}\Big\}$
$=\Big\{\frac{(100+15)}{100}\times\text{x}\Big\}$
$=\frac{115}{100}\text{x}$
$=\text{Rs. }\frac{23}{20}\text{x}$
$=\text{x}\times\frac{120}{100}$
$=\text{Rs. }\frac{6}{5}\text{x}$
$\frac{6}{5}\text{x}-\frac{23}{20}\text{x}=108$
$\Rightarrow\frac{24\text{x}-23\text{x}}{20}=108$
$\Rightarrow\frac{\text{x}}{20}=108$
$\text{x}=2160$ Hence, the cost price of the tricycle is $Rs. 2160$

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Question 65 Marks

By selling $8$ dozen pencils, a shopkeeper gains the selling price of one dozen pencils. Find his gain percent.

Answer

Let the $CP$ of one pencil be $Rs. x$
Therefore, the $CP$ of $96$ pencils will be $Rs. 96x$
Let SP of one pencil be $Rs. y$
$\therefore SP$ of $96$ pencils $= Rs. 96y$
Gain$= SP$ of one dozen pencil $= Rs.12y$ (given)
Gain $= SP - CP $
$\Rightarrow 12y = 96x - 96y $
$\Rightarrow 96x = 96y - 12y $
$\Rightarrow 96y = 84y$
$\Rightarrow\text{x}=\frac{84}{96}\text{y}$
$\text{Gain%}=\Big(\frac{\text{Gain}}{\text{CP}}\times100\Big)\%$
$=\Big(\frac{12\text{y}}{96\text{x}}\times100\Big)\%$
$=\Big(\frac{12\text{y}\times96}{96\times84\text{y}}\times100\Big)\%$
$=14.28\%$

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Question 75 Marks

On selling a sofa-set for $Rs. 21600$, a dealer gains $8\%$. For how much did he purchase it?

Answer

$SP$ of sofa set $= Rs. 21600$ Gain $= 8\%$
$\text{CP}=\frac{\text{SP}\times100}{100+\text{gain%}}$
$=\frac{21600\times100}{100+8}$
$=\text{Rs. }\frac{21600\times100}{108}$
$=\text{Rs. }20000$

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Question 85 Marks

Sandeep sold a television at a loss of $8\%$. If he had sold it for $Rs. 3360$ more, he would have gained $6\%$. For how much did Sandeep buy it?

Answer

Let the $CP$ of the television be $Rs. x$
$\text{SP at 8% loss}=\frac{(100-8)}{100}\times\text{x}$
$=\text{Rs. }\frac{92}{100}\text{x}$
$\text{SP at 6% gain}=\frac{100+6}{100}\times\text{x}$
$=\text{Rs. }\frac{106}{100}\text{x}$
$=\frac{106}{100}\text{x}-\frac{92}{100}\text{x}=3360$
$\Rightarrow\frac{14}{100}\text{x}=3360$
$\Rightarrow\text{x}=\frac{336000}{14}=24000$
$\therefore CP - Rs. 24000$ Sandeep bought it at the cost of $Rs. 24000$

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Question 95 Marks

By selling $3 6$ oranges, a vendor suffers a loss equal to the selling price of $4$ oranges. Find his loss percent.

Answer

Let the $CP$ of $1$ orange be $Rs. x$
$\therefore CP$ of $36$ orange $= Rs. 36x$
Let SP of orange be $Rs. y$
$\therefore SP$ of $36$ oranges $= Rs. 36y$
Loss $= SP$ of $4$ oranges $= 4y$ (given)
We kwno: Loss $= CP - SP $
$\Rightarrow 4y = 36x - 36y $
$\Rightarrow 4y + 36y = 36x $
$\Rightarrow 40y = 36x $
$\Rightarrow 10y = 9x$
$\Rightarrow\text{y}=\frac{9}{10}\text{x}$
$\text{Loss%}=\Big(\frac{\text{Loss}}{\text{CP}\times100}\Big)\%$
$=\Big(\frac{4\text{y}}{36\text{x}}\times100\Big)\%$
$=\Big(\frac{4\times9\text{x}}{36\text{x}\times10}\times100\Big)\%$
$=10\%$ Loss$\% = 10\%$

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Question 105 Marks

Pankaj sells two cycles for $Rs. 2376$ each. On one he gains $10\%$ and on the other he loses $10\%$. Find his gain or loss percent.

Answer

$SP$ of first cycle $= Rs. 2376$ Gain $= 10%$
$\therefore\text{CP of first cycle}=\frac{\text{SP}\times100}{100+\text{gain%}}$
$=\text{Rs. }\frac{2376\times100}{100+10}$
$=\text{Rs. }\frac{2376\times100}{110}$
$=\text{Rs. }2160$ In second case, $SP$ of
second cycle $= Rs. 2376$ And loss $= 10\%$
$\therefore\text{CP of second cycle = Rs. }\frac{2376\times100}{100-10}$
$=\text{Rs. }\frac{2376\times100}{90}$
$=\text{Rs. }2640$
$\therefore$ Total SP of two cycle $= Rs. 2376 \times 2 = Rs. 4752$ And
$CP = 2160 + 2640 = Rs. 4800$
Loss $= CP - SP = Rs. 4800 - 4752 = Rs. 48$
$\therefore\text{ Loss%}=\frac{\text{Loss}\times100}{\text{CP}}$
$=\frac{48\times100}{4800}$
$=1\%$

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