Question

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

• A. 99%
• B. 85%
• C. 75.5%
• D. 65%

Answer 1

The correct option is C

75.5%

Let the marked price of an article be ₹ X and a single discount of $d\%$ be equivalent to two given successive discounts of $50\%$ and $49\%$

Then,

$(1-\frac{d}{100})of₹x=(1-\frac{50}{100})(1-\frac{49}{100})of₹x$ [Both S.P must be equal]

$\Rightarrow 200-2d=51$

$\Rightarrow 2d=149$

$\Rightarrow d=74.5\%$

Hence, a single discount of $74.5\%$ is equivalent to two given successive discounts.