# Difficult Percentages Solved QuestionAptitude Discussion

 Q. A salesman sells two kinds of trousers: cotton and woollen. A pair of cotton trousers is sold at $30\%$ profit and a pair of woollen trousers is sold at $50\%$ profit. The salesman has calculated that if he sells $100\%$ more woollen trousers than cotton trousers, his overall profit will be $45\%$. However, he ends up selling $50\%$ more cotton trousers than woollen trousers. What will be his overall profit?
 ✖ A. $37.5\%$ ✔ B. $40\%$ ✖ C. $41\%$ ✖ D. $42.33\%$

Solution:
Option(B) is correct

Let the cost price of 1 cotton trouser and 1 woollen trouser be ‘$C$’ and ‘$W$’ respectively.

Case I: Number of woollen trousers sold is $100\%$ more than cotton trousers.

Let us calculate profit keeping one unit of a cotton trouser.

$1.3C+1.5\times 2\times W=1.45(C+2W)$

$\Rightarrow0.15C=0.1W$

$\Rightarrow3C=2W$

Case II: Number of cotton trousers sold is $50\%$ more than woollen trousers.

Here, we will calculate sales price keeping one unit of a cotton trouser as we did in the case I. Now as per the condition given, cotton trousers sold is $50\%$ more than woollen trousers.

$\Rightarrow$ for every woollen trouser $1.5$ $\left(=\dfrac{3}{2}\right)$  cotton trousers are being sold.

$\Rightarrow$ for every cotton trouser $\dfrac{2}{3}$ $\left(=\dfrac{1}{3/2}\right)$  woollen trousers are being sold.

$S.P.=1.3C+1.5\times \dfrac{2W}{3}$

$\Rightarrow S.P.=1.3C+W=2.8C$

$\Rightarrow CP=C+\dfrac{2}{3}\times W$

$=2C$

Profit

$=\dfrac{2.8C-2C}{2C}\times 100$

$=\textbf{40%}$

## (4) Comment(s)

Anu
()

In case 1 how is it 1.45??please someone tell

Gourab Mukherjee
()

It says "if he sells 100% more woolen trousers than cotton trousers, his overall profit will be 45%". SO therefore if he sells C quantities of cotton, then he sells twice the number woolen clothes. the total profit in this case is 45%, which is basically (1+45/100)*C.P. You Should know that S.P=(1+x/100)*C.P where x is the profit percentage.

Arun
()

Why is $CP=C+(2/3)W = 2C$

Shouldn't it be $CP=C+W=C+(3/2)C=2.5C$ ?

Shireen
()

No, it shouldn't be. CP is calculated keeping ONE unit of $C$ and since condition says, number of cotton trousers sold is 50% more than woollen trousers, which means for every $1 C$ there will be $\frac{2}{3}W$