Ajay sold a shirt at 8% gain, had it been sold for Rs.75 more, the gain would have been 14%. Find the cost price of the jacket.

Hint: Assume C.P. and S.P. as the cost price and selling price of the jacket. Consider two cases and use the formula for profit percentage given as: - Profit % = \[\left( \dfrac{S.P-C.P}{C.P} \right)\times 100%\] to form two relations between C.P. and S.P. Use the substitution method to solve for the value of C.P. for the jacket. In the second case, take the value of the selling price equal to (S.P. + 75).

Complete step-by-step answer:
Here, let us assume the cost price and selling price of the jacket as C.P. and S.P. respectively. We have to find the value of C.P. of the jacket. Now, we have been provided with two cases, so let us consider them one – by – one.
Case 1: - Here, it is given that the gain% on the jacket is 8% for the original values of C.P. and S.P.
Now, applying the formula for profit percent given as: -
Profit % = \[\left( \dfrac{S.P-C.P}{C.P} \right)\times 100%\], we get,
\[\begin{align}
  & \Rightarrow 8\%=\left( \dfrac{S.P-C.P}{C.P} \right)\times 100\% \\
 & \Rightarrow \dfrac{8}{100}=\left( \dfrac{S.P}{C.P}-\dfrac{C.P}{C.P} \right) \\
 & \Rightarrow \dfrac{8}{100}=\left( \dfrac{S.P}{C.P}-1 \right) \\
\end{align}\]
\[\Rightarrow \dfrac{S.P}{C.P}=\left( 1+\dfrac{8}{100} \right)\] - (1)
Case 2: - Here, it is given that if Ajay increases the selling price by Rs.75, then the gain % will become 14%. So, we have,
New selling price of the jacket = S.P. + 75
So, applying the formula for profit percent given as: -
Profit % = \[\left( \dfrac{S.P-C.P}{C.P} \right)\times 100%\], we get,
\[\Rightarrow 14%=\left( \dfrac{S.P+75-C.P}{C.P} \right)\times 100%\]
\[\begin{align}
  & \Rightarrow \dfrac{14}{100}=\left( \dfrac{S.P}{C.P}+\dfrac{75}{C.P}-\dfrac{C.P}{C.P} \right) \\
 & \Rightarrow \dfrac{14}{100}=\left( \dfrac{S.P}{C.P}+\dfrac{75}{C.P}-1 \right) \\
\end{align}\]
Substituting the value of \[\dfrac{S.P}{C.P}\] from equation (1) in the above equation, we get,
\[\begin{align}
  & \Rightarrow \dfrac{14}{100}=\left( 1+\dfrac{8}{100}+\dfrac{75}{C.P}-1 \right) \\
 & \Rightarrow \dfrac{14}{100}=\dfrac{8}{100}+\dfrac{75}{C.P} \\
 & \Rightarrow \dfrac{75}{C.P}=\dfrac{14}{100}-\dfrac{8}{100} \\
 & \Rightarrow \dfrac{75}{C.P}=\dfrac{6}{100} \\
\end{align}\]
By cross – multiplication we get,
\[\Rightarrow C.P=\dfrac{75\times 100}{6}\]
\[\Rightarrow \] C.P. = Rs.1250
Hence, the cost price of the jacket is Rs.1250.

Note: One must not try to calculate the selling price of the jacket using the obtained relations because it is of no use here. You may note that in the formula of profit percent we have C.P. in the denominator, this is because profit percent is always considered on the cost price and not the selling price. You may see that the selling price of jacket in case 2 is Rs.75 more than that of the original S.P. as it was provided in the question. Remember the formulas of profit% to solve the question.