Simple interest on a certain sum at a certain amount and rate of interest is 25

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Question

Simple interest on a certain sum at a certain amount and rate of interest is 25/16 of the sum. If the numbers representing rate percent and time in years be equal than rate percent per annum is?

Options:

A . 8 %

B . 11 ½ %

C . 12 ¼ %

D . 12 ½ %

Answer: Option D

Let the sum be Rs x , Rate = R % p.a, Time = R years
S. I = Rs 25x/16
R = 100 Ã— 25x/16 Ã— 1/x Ã—1/R
=> R² = 2500/16
=> R = 50/4 = 25/2
Hence Rate = 12 ½ % p.a

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