4 Mark Question

Question 14 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 24 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 × 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 34 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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