Question

If the selling price of a flower vase is $ \dfrac{5}{6} $ of its cost price, find the loss percent?

Answer 1

Hint: Let us assume that the cost price (C.P.) of a flower is x then selling price (S.P.) of the flower vase is $ \dfrac{5}{6}x $ . Loss is calculated using the formula $ C.P.-S.P. $ and to calculate the loss percent divide this loss by $ C.P. $ and multiply this division by 100. Substitute the value of cost price and selling price of the flower vase in the formula, you will get the loss percent.

Complete step-by-step answer:
Let us assume that the cost price of the flower vase (C.P.) is Rs x.
It is given that the selling price of a flower vase (S.P.) is $ \dfrac{5}{6} $ of its cost price so we can write selling price in terms of x is $ \dfrac{5}{6}x $ .
We know that loss is equal to the subtraction of selling price from the cost price.
 $ \text{Loss}=C.P.-S.P. $
We are asked to find the loss percent which we are going to calculate by dividing the loss that we have calculated above to the cost price of the vase and then multiply this result of division by 100.
 $ \text{Loss percent}=\dfrac{Loss}{C.P.}\times 100 $
Substituting the value of cost price as x and selling price as $ \dfrac{5}{6}x $ in the above equation we get,
 $ \text{Loss percent}=\dfrac{x-\dfrac{5}{6}x}{x}\times 100 $
Taking x common from the numerator we get,
 $ \text{Loss percent}=\dfrac{x\left( 1-\dfrac{5}{6} \right)}{x}\times 100 $
In the above equation, x will be cancelled out from the numerator and the denominator of the right hand side of the equation.
 $ \text{Loss percent}=\left( 1-\dfrac{5}{6} \right)\times 100 $
Taking 6 as the L.C.M on the right hand side of the above equation we get,
 $ \begin{align}
  & \text{Loss percent}=\left( \dfrac{6-5}{6} \right)\times 100 \\
 & \Rightarrow \text{Loss percent}=\dfrac{1}{6}\times 100 \\
 & \Rightarrow \text{Loss percent}=\dfrac{50}{3}=16.66\% \\
\end{align} $
From the above solution the loss percent that we have obtained is 16.66%.

Note: You might get confused between the formulas of profit and loss when the cost price comes first and when the selling price comes first in the two formulas.
 $ \text{Profit}=S.P.-C.P. $
 $ \text{Loss}=C.P.-S.P. $
When loss will occur then the cost price is always greater than the selling price and we cannot make our answer negative so in loss we subtract the selling price from the cost price.
Whereas when profit occurs then the selling price is always greater than the cost price so in the formula of profit percent we subtract cost price from the selling price.