Question : If successive discounts of 5%, 10%, and p% are equivalent to a single discount of 31.6%, the value of p is:
Option 1: 15
Option 2: 25
Option 3: 20
Option 4: 30
Correct Answer: 20
Solution :
Single equivalent discount = $(a+b–\frac{a×b}{100})\%$, where $a$% and $b$% are two successive discounts.
Single discount of 5% and 10% $= 5 + 10 - \frac{(50)}{100}=14.5$
Now, single discount of 14.5% and $p$% $= 14.5 + p - \frac{(14.5p)}{100}$
According to the question,
$14.5 + p - \frac{(14.5p)}{100} = 31.6$
$⇒p - 0.145p = 17.1$
$⇒0.855p = 17.1$
$\therefore p = 20\%$
Hence, the correct answer is 20%.
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