5 Marks Questions

Question 15 Marks

By selling an article for $Rs. 240$, a man makes a profit of $20\%$. What is his $C.P.?$ What would his profit percent be if he sold the article for $Rs. 275?$

Answer

Let $CP = Rs. x, SP = Rs. 240$
Let profit be $Rs. P.$
Now, profit $\% = 20\%$
Since Profit $\% =\frac{\text{Profit}}{\text{CP}}\times10$
$\Rightarrow20=\frac{\text{P}}{\text{x}}\times100$
$\Rightarrow\text{P}=\frac{20\text{x}}{100}$
$\Rightarrow\text{P}=\frac{\text{x}}{5}$
Profit $= SP - CP = 240 - x$
$\Rightarrow P = 240 - x$
$\Rightarrow\frac{\text{x}}{5}=240-\text{x}$
$\Rightarrow240=\frac{\text{x}}{5}+\text{x}$
$\Rightarrow240=\frac{6\text{x}}{5}$
$\Rightarrow\text{x}=\frac{1200}{6}$
$\Rightarrow\text{x}=200$
So, $CP = Rs. 200$
New $SP = Rs. 275$ and $CP = Rs. 200$
Profit % $=\Big(\frac{\text{SP}\ -\ \text{CP}}{\text{CP}}\Big)\times100$
$=\Big(\frac{275\ -\ 200}{200}\Big)\times100$
$=\frac{75}{200}\times100$
$=\frac{7500}{200}$
$=37.5\%$

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Question 25 Marks

A flowerist buys $100$ dozen roses at $Rs. 2$ a dozen. By the time the flowers are delivered, $20$ dozen roses are multilated and are thrown away. At what price should he sell the rest if he needs to make a $20\%$ profit on his purchase?

Answer

Cost of $1$
dozen roses $= Rs. 2$
Number of roses bought by the florist $= 100$
dozens Thus, cost price of $100$
dozen roses $= 2 \times 100 = Rs. 200$
Roses left after discarding the mutilated ones $= 80$
dozens Calculating the price at which the florist should sell the $80$
dozen roses in order to make a profit of $20\%$,
we have Profit % $=\Big(\frac{\text{SP}\ -\ \text{CP}}{\text{CP}}\Big)\times100$
$20=\Big(\frac{\text{SP}\ -\ 200}{200}\Big)\times100$
$40 = SP - 200 SP = Rs. 240$
Therefore, the $SP$ of the roses should be $\text{Rs.}\frac{240}{80}=\text{Rs. }3$ per dozen.

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Question 35 Marks

Harish purchased $50$ dozen bananas for $Rs. 135$. Five dozen bananas could not be sold because they were rotten. At what price per dozen should Harish sell the remaining bananas so that he makes a profit of $20\%?$

Answer

Cost price of $50$ dozens bananas that Harish purchased, $CP = Rs. 135$
Bananas left after removing $5$ dozen rotten bananas $= 45$
dozens Effective $CP$ of one dozen bananas $=\text{Rs.}\frac{135}{45} = \text{Rs. }3$
Calculating the price at which Harish should sell each dozen bananas to make a profit of $20\%,$
we get Profit $\% =\Big(\frac{\text{Gain}}{\text{CP}}\Big)\times100$ To get a gain of $20\%$
we give profit $\% = 20$ and substitute, $20=\Big(\frac{\text{Gain}}{135}\Big)\times100$ $\text{Gain}=\frac{270}{10}=27$
We know; $SP = CP +$ Gain $SP = 27 + 135 SP = 162$
Now, that $SP$ is for $45$ Dozens of bananas Calculating for one dozen $=\frac{162}{45}=\text{Rs. }3.6$
Harish should sell the bananas at $Rs. 3.60$ a dozen in order to make a profit of $20\%.$

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