If successive discounts of 5%, 10%, and p% are equivalent to a single discount of 31.6%, then the value of p is:
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Correct answer: C
Explanation
The correct answer is option 3 i.e. 20.
If successive discounts of 5%, 10%, and p% are equivalent to a single discount of 31.6%
The single discount equivalent to the successive discount of x% and y% = x+ y - xy/100
According to the question;
Equivalent discount (5% and 10%) = 5 + 10 - (5 × 10)/100 = 15 - 0.5 = 14.5%
Equivalent discount (14.5% and p%) = 14.5 + p - (14.5 × p)/100 = 14.5 + 0.855p
⇒ 14.5 + 0.855p = 31.6
⇒ 0.855p = 31.6 - 14.5
⇒ p = 17.1/0.855 = 20