Question

Find C.P. if S.P. is equal to Rs. 1128 and loss is 6%.

Answer 1

Hint: We explain the terms C.P. and S.P. Then we assume the C.P. We know that the added value of the loss and the selling price is equal to the cost price. We find the respective values and form an equation to solve it. The solution gives the value of the C.P.

Complete step-by-step solution:
The C.P. and S.P. stands for cost price and the selling price. It is given that S.P. is Rs. 1128 and the loss is 6%.
Let us assume the C.P. to be Rs. $x$. We know for any arbitrary percentage value of a%, we can write it as $\dfrac{a}{100}$. The percentage is to find the respective value out of 100.
The loss is 6% on $x$. So, $x\times \dfrac{6}{100}=\dfrac{6x}{100}$ is the loss amount.
The selling price is Rs. 1128.
As the sale was a loss, it was sold at a lesser price than the cost price.
We know that the added value of the loss and the selling price is equal to the cost price.
We know that the loss% is = $\dfrac{\text{C.P-S.P}}{C.P}\times 100$
On simplifying we get C.P = $S.P+\dfrac{\text{loss}\%}{100}\times C.P$
The equation gives $1128+\dfrac{6x}{100}=x$.
We solve the equation to find the value of $x$.
\[\begin{align}
  & x-\dfrac{6x}{100}=1128 \\
 & \Rightarrow \dfrac{94x}{100}=1128 \\
 & \Rightarrow x=\dfrac{1128\times 100}{94}=1200 \\
\end{align}\]
The cost price is Rs. 1200.

Note: The loss and gain are always considered with respect to the cost price. The gain happens when the selling price is greater than the cost price. The value of the fraction is actually the unitary value of 6 out of 100. Therefore, in percentage value we got 6 as the percentage.