Question

You want to sell a cosmetics for Rs. $119$ and gains as much percent as the cost price of the cosmetics. Find the gain $\%$ of the cosmetics.

• A. $21$
• B. $49$
• C. $56$
• D. $43$

Answer 1

The correct option is B $49$

Let the C.P. of the cosmetics be $x$
Gain $\%=x\%$ of $x=$ $\frac{x^2}{100}$
S.P. $=$ C.P. $+$ gain
S.P. $=119$
Therefore, $x+\frac{x^2}{100}=119$

Simplify further,
$100x+x^2=11900$
$x^2+100x-11900=0$
$(x+170)(x-70)=0$
$x=-170$ or $70$
Price cannot be negative, hence $x=70$
Gain $\%=x\%$ of $x$
$=$ $\frac{70}{100}\times 70$
$=49$

Hence option (B) is corrcet