Question

By selling 125 cassettes, a man gains an amount equal to the selling price of 5 cassettes. Find the gain percent.

Answer 1

Hint: Assume the selling price of one cassette as x and using the unitary method find the selling price of 125 cassettes and hence use the formula: - Profit = S.P – C.P, to find the value of C.P., where S.P. denotes selling price and C.P. denotes the cost price of 125 cassettes. Now, apply the formula: - Profit% = \[\dfrac{S.P.-C.P.}{C.P.}\times 100%\] to find the answer.

Complete step by step answer:
Here, we have been provided with the information that a man gains an amount equal to the selling price of 5 cassettes when he sold 125 cassettes. We have to find the profit percent. But first, we need to calculate the cost price.
Now, let us assume the selling price of one cassette as x. So, using unitary method, we have,
\[\Rightarrow \] Selling price (S.P.) of 125 cassettes = 125x
\[\Rightarrow \] Profit on these 125 cassettes = 5x
We know that when the selling price of an article is more than its cost price then profit occurs. So, applying the formula for profit given as: - Profit = S.P. – C.P., where, S.P. is selling price and C.P. is cost price, we have,
\[\begin{align}
  & \Rightarrow 5x=125x-C.P. \\
 & \Rightarrow C.P.=125x-5x \\
 & \Rightarrow C.P.=120x \\
\end{align}\]
Now, we know that profit percent is given as: - Profit% = \[\dfrac{S.P.-C.P.}{C.P.}\times 100%\]. So, applying this formula and substituting the obtained values of S.P. and C.P., we have,
\[\Rightarrow \] Profit% = \[\dfrac{125x-120x}{120x}\times 100%\]
\[\Rightarrow \] Profit% = \[\dfrac{5x}{120x}\times 100%\]
Cancelling the common factors, we get,
\[\Rightarrow \] Profit% = \[\dfrac{25}{6}%\]
\[\Rightarrow \] Profit% = 4.167% (rounded off value)
Hence the man obtained a gain percent of 4.167% by selling 125 cassettes.

Note:
One may note that we cannot assume the cost price of the cassette as ‘x’ at the initial step of the solution because we do not know the number of cassettes that were purchased by the man. We have only been provided with information regarding the selling of cassettes. You must remember the formulas of profit and profit% to solve the question. You may see that in the formula of profit% we have C.P. in the denominator. This is because profit is always found on C.P. and not S.P., and that is why we needed to calculate the value of C.P.