Question

Find the single discount equivalent to two successive discounts $50\%$ and $49\%$.

• A. 99%
• B. 85%
• C. 75.5%
• D. 65%

Answer 1

Answer: (C)

($74.5)\%$

Let the marked price of an article be $Rs.100$ and
Given two given successive discounts $d_1=50\%$ and $d_2=49\%$

Then, $\text{S.P = M.P}\times \frac{100-d_1}{100}\times \frac{100-d_2}{100}$

$=100\times \frac{100-50}{100}\times \frac{100-49}{100}$

$=100\times \frac{50}{100}\times \frac{51}{100}$

$=\frac{255}{10}$

$=Rs.25.5$
$\therefore$ Single equivalent discount $=100-25.5=74.5\%$
Hence, a single discount of $74.5\%$ is equivalent to two given successive discounts.