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# By selling 144 hens Mahesh suffered a loss equal to the selling price of 6 hens. Find his loss per cent? Verified
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Hint: We will have to find the selling price and cost price of a hen. Loss is calculated by, Loss=CP-SP and profit is calculated by Profit=SP-CP because when there is loss, cost price is greater than selling price and vice versa for profit. And Loss per cent is calculated by Loss percent=$\dfrac{CP-SP}{CP}\times 100$ .

First let us assume that the cost price of a hen is CP and selling price is SP.
Loss of one item is calculated by, Loss=CP-SP
Selling price of 144 hens=144SP.
Cost price of 144 hens=144CP.
Selling price of 6 hens=6SP.
Cost price of 6 hens=6CP.
Loss by selling 144 hens=144CP-144SP=144(CP-SP).
From the question we have,
Loss by selling 144 hens= selling price of 6 hens
144(CP-SP)=6SP
Adding 144SP both sides we have,
144CP=6SP+144SP
144CP=150SP
Therefore, $SP=\dfrac{144}{150}CP$ …….(i)

Now we have,
Loss per cent= $\dfrac{Loss}{CP}\times 100$
Since, Loss=CP-SP, we have
Loss per cent= $\dfrac{CP-SP}{CP}\times 100$
Substituting the value of SP from equation (i) we have,
Loss per cent= $\dfrac{CP-\dfrac{144}{150}CP}{CP}\times 100$
Cancelling CP from both numerator and denominator we have,
Loss per cent= $\dfrac{1-\dfrac{144}{150}}{1}\times 100$
$=\left( 1-\dfrac{144}{150} \right)\times 100$
Taking 150 as LCM we have,
$=\left( \dfrac{150-144}{150} \right)\times 100$
$=\dfrac{6}{150}\times 100$
On simplifying we get,
Loss per cent= 4