Question

# By selling 144 hens Mahesh suffered a loss equal to the selling price of 6 hens. Find his loss per cent?

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

Hence, the answer is 4%.

Note: We must always remember that Loss per cent of any number of items is equal but Loss varies with the number of items. Therefore, from the starting we were clear that SP and CP were selling price and cost price of one hen otherwise our calculations may contain an error as we proceeded. And when calculating loss per cent the denominator must be CP because whenever we calculate percentage the denominator is always the original value of the item and here the CP was our original value.