Question

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 1

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 $=Rs.\frac{135}{45}=Rs.3$
Calculating the price at which Harish should sell each dozen bananas to make a profit of $20\%,$ we get
Profit $\%=\frac{Gain}{CP}\times 100=\frac{(SP-CP)}{CP}\times 100\%$

$20\%=\frac{SP-3}{3}\times 100\%$

$\Rightarrow \frac{1}{5}=\frac{SP-3}{3}$

$\Rightarrow 3=5SP-15$

$\Rightarrow SP=\frac{18}{5}=Rs.3.60$
Harish should sell the bananas at $Rs.3.60$ a dozen in order to make a profit of $20\%$.