Question

Jai Pal sells a shirt at a profit of $25$ percent. Had he bought it at $25$ percent less and sold it for Rs. $25$ less he still would have gained $25$ percent. The cost price of the shirt is

• A. Rs. $50$
• B. Rs. $75$
• C. Rs. $80$
• D. Rs. $100$

Answer 1

Answer: (C)

Rs. $80$

Let the CP of the shirt $=x$ in $\text{Rs.}$

Then profit at $25\%=$ $x\times \frac{25}{100}=\frac{x}{4}$

So the SP $=$ $x+\frac{x}{4}=\frac{5x}{4}$

In the second case, the CP & the SP are decreased by $25\%$ & $\text{Rs.}25$ respectively.

So the new CP $=$ $x-\frac{x}{4}=\frac{3x}{4}$ and

the new SP $=$ $\frac{5x}{4}-25=\frac{5X-100}{4}$

Then the new profit $=$ $\frac{5x-100}{4}-\frac{3x}{4}=\frac{2x-100}{4}$

$\therefore$ The profit percent $=$ $(\frac{2x-100}{4}÷\frac{3x}{4})\times 100$

So, by the given condition, we have

$(\frac{2x-100}{4}÷\frac{3x}{4})\times 100=25$

$\Rightarrow \frac{2x-100}{3x}=\frac{1}{4}$

$\Rightarrow 8x-400=3x$

$\Rightarrow 5x=400$

$\Rightarrow x=80$

So the cost price of the shirt $=$ $\text{Rs.}80$