Question

If the C.P. of 10 articles is equal to the S.P. of 12 articles. Find the gain or loss \[\% \] .

Answer 1

Hint: Let the C.P. of 1 article be x \[ \Rightarrow \] C.P. of 10 articles is 10x. It is given that; C.P. of 10 articles = S.P. of 12 articles. Using that, find the S.P. in terms of x. Compare S.P. and C.P. and decide whether it is a gain or a loss.

Complete step-by-step answer:
Let the C.P. of 1 article be x.
So, the C.P. of 10 articles is 10x.
It is given that; C.P. of 10 articles = S.P. of 12 articles = 10x.
Now, the S.P. of 12 articles = 10x.
Therefore, the S.P. of 1 articles is \[\dfrac{{10x}}{{12}} = \dfrac{{5x}}{6}\] .
Here, C.P. \[ > \] S.P. Hence, it is a loss.
\[\therefore \]Loss \[ = \] C.P. – S.P.

\[= x - \dfrac{{5x}}{6} \]

\[x = \dfrac{{6x - 5x}}{6} \]

\[x = \dfrac{x}{6} \]

Now, for loss \[\% \]
Loss \[\% \] \[ = \left( {\dfrac{{{\text{Loss}}}}{{{\text{C}}{\text{.P}}{\text{.}}}}} \right){{ \times }}100\% \]

\[ = \left( {\dfrac{{\dfrac{x}{6}}}{x}} \right) \times 100\% \]

\[ = \dfrac{1}{6} \times 100\% \]

\[ = 16.67\% \]

Hence, the answer is It is a loss. Loss \[\% \] = \[16.67\% \] .

Note: If the S.P. is greater than the C.P., then it is considered to be a profit or gain. The formula to calculate profit is Profit = C.P. – S.P.
If the C.P. is greater than the S.P., then it is considered to be a loss. The formula to calculate loss is Loss = S.P. – C.P.
If the C.P. is neither greater than nor smaller than S.P., i.e. C.P. is equal to S.P., then it is neither considered a profit nor a loss.