Question

Two successive discounts of $10\%$ and $5\%$ are equal to a single discount of

• A. $15$%
• B. $7\frac{1}{2}$%
• C. $12$%
• D. $14\frac{1}{2}$%

Answer 1

The correct option is D $\left(14\frac{1}{2}\right)$%

Let the total amount be $=Rs.100$
After $10\%$ discount on $100$, we get
$=\frac{10}{100}\times 100$
$=Rs.10$
Amount remaining after $10\%$ discount is $100-10=Rs.90$
Now, $5\%$ discount on $Rs.90$ is $=\frac{5}{100}\times 90$
$=\frac{9}{2}$
$=4.5$
Thus, the amount remaining after second discount is $90-4.5=Rs.85.5$
Therefore, the total discount amount of the two successive discount $=100-85.5=Rs.14.5$
Hence, the single discount is $=\frac{14.5}{100}\times 100$
$=14.5\%$