Question : Find the single discount equivalent to two successive discounts of 10% and 5%.
Option 1: 85.5%
Option 2: 90%
Option 3: 75.5%
Option 4: 14.5%
Correct Answer: 14.5%
Solution :
When two discounts are given successively, the equivalent single discount is,
$D = 100 -\frac{(100 - d_1) \times (100 - d_2) }{ 100}$
Where D is the equivalent single discount, and $d_1$ and $d_2$ are the two successive discounts.
$D = 100 -\frac{(100 - 10) \times (100 - 5) }{ 100}
= 100 - \frac{(90) \times (95) }{ 100}
= 100 - \frac{171 }{2}
= \frac{29 }{2} = 14.5$
Hence, the correct answer is 14.5%.
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