Simple interest on a certain sum at a certain rate is 9/16

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Simple interest on a certain sum at a certain rate is 9/16 of the sum. If the number representing rate percent and time in years be equal. Then the time is ?

1. 5¹/₂years
2. 6¹/₂years
3. 6¹/₄years
4. 7¹/₂years

Correct Option: D

Let principle = P, then SI = (9/16) x P.
Let rate = R% per annum and time = R years
Then, 9/16 P = P x R x R / 100
⇒ R² = 900/16
∴ R = 30/4 = 7¹/₂ years