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Maths 4 Mark Question

SimpleProfit and Loss · Maharashtra Board STD 7 (MSBSHSE - Semi English Medium). 9 questions.

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Question 14 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 24 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 34 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 44 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 54 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 64 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
⇒ 12y = 96x - 96y
⇒ 96x = 96y - 12y
⇒ 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 74 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 84 Marks
Sandeep sold a television at a loss of 8%. If he had sold it forRs. 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. 24000Sandeep bought it at the cost of Rs. 24000
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Question 94 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
⇒ 4y = 36x - 36y
⇒ 4y + 36y = 36x
⇒ 40y = 36x
⇒ 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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