Question

A single discount equivalent to successive discounts of $30\%,20\%$ and $10\%$ is

• A. $50\%$
• B. $51\%$
• C. $49.4\%$
• D. $49.6\%$

Answer 1

The correct option is D $49.6\%$

Let the M.P. $=$ Rs. $100$
Then, S.P. after $1^{st}$ discount of $30\%$
$=100-30\%$ of Rs. $100=100-\frac{30}{100}\times 100=$ Rs. $70$
S.P. after $2^{nd}$ discount of $20\%$
$\Rightarrow 70-$ $20\%$ of Rs. $70=70-\frac{20}{100}\times 70$
$\Rightarrow 70-14=$ Rs. $56$
Net S.P. after $3^{rd}$ discount of $10\%$
$=56-10\%$ of Rs. $56=56-\frac{10}{100}\times 56$

$\Rightarrow 56-5.60=$ Rs. $50.4$
$\therefore$ Total discount $=$ Rs. $100-$ Rs. $50.4=$ Rs. $49.6$
Discount rate $=\frac{49.6}{100}\times 100=49.6\%$