Question

# By selling 45 lemons for Rs.40, a man loses 20%. How many should he sell for Rs.24 to gain 20% in the transaction?

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Hint: Here, we will use the formulae of cost price and selling price with gain and loss percentages to solve the given problem.
Given,
Selling Price of 45 is Rs.40 and he loses 20%. Now, let us find the cost price of these 45 lemons by using the formulae of cost price with loss percentage i.e..,
$C.P = \dfrac{{S.P\times 100}}{{(100 - loss\% )}} \to (1)$
Now, let us substitute the value of S.P and loss% in equation (1), we get
$C.P = \dfrac{{45\times 100}}{{(100 - 20)}} = \dfrac{{45\times 100}}{{80}} = 50$
Therefore, the Cost price of 45 lemons is Rs.50. Now, let us find the Selling price of 45 lemons with
20% gain by using the formulae of selling price with gain percentage i.e..,
$S.P = \dfrac{{C.P\times (100 + gain\% )}}{{100}} \to (2)$
Now, let us substitute the value of C.P and gain% in equation (2), we get
$S.P = \dfrac{{50\times (100 + 20)}}{{100}} = \dfrac{{50\times 120}}{{100}} = 60$
Since, the selling price of 45 lemons with 20% gain is Rs.60, then the selling price of 1 lemon will be $\dfrac{{60}}{{45}} = \dfrac{4}{3}$. Let ‘x’ be the number of lemons then the number of lemons he sell at Rs.24 will be
$\Rightarrow \dfrac{4}{3}\times x = 24 \\ \Rightarrow x = 24\times \dfrac{3}{4} \\ \Rightarrow x = 18 \\$
Hence, the number of lemons he can sell at Rs.24 with 20% gain is 18.
Note: Make sure that percentage of gain should be added to ‘100’ whereas the percentage of loss is subtracted from ‘100’.