Question

A shirt was sold at a profit of 15$\%$. If its cost had been 5$\%$ less and it had been sold for Rs. 21 less, then the profit would have been 10$\%$. Find the cost of the shirt.

• A. $Rs.210$
• B. $Rs.220$
• C. $Rs.100$
• D. $Rs.200$

Answer 1

The correct option is D $Rs.200$

Given that:

A shirt was sold at a profit of $15\%$.

If the cost had been $5\%$ less, and it had been sold for $Rs.21$ less, then the profit would have been $10\%$.

To find out:

The cost of the shirt.

Let the cost of the shirt be $Rs.x$.

We know that, $S.P.=\frac{(profit\%+100)C.P.}{100}$

Here, $profit\%=15$

$\therefore S.P.=\frac{(15+100)x}{100}$

$\Rightarrow S.P.=1.15x$

Now, if the cost is $5\%$ less, then,

$C.P.=95\%ofx$

$\Rightarrow C.P.=\frac{95}{100}x$

$\therefore C.P.=0.95x$

Also, the selling price is $Rs.21$ less.

$\therefore S.P.=1.15x-21$

In this case, the profit would have been $10\%$, as given in the problem.

Now, we know that, $profit\%=\frac{S.P.-C.P.}{C.P.}\times 100$

$\therefore 10=\frac{(1.15x-21)-0.95x}{0.95x}\times 100$

$\Rightarrow 10=\frac{1.15x-21-0.95x}{0.95x}\times 100$

$\Rightarrow 10\times 0.95x=(0.20x-21)\times 100$

$\Rightarrow 9.5x=20x-2100$

$\Rightarrow 20x-9.5x=2100$

$\Rightarrow 10.5x=2100$

$\Rightarrow x=\frac{2100}{10.5}$

$\therefore x=Rs.200$

Hence, the cost of the shirt is $Rs.200$.