[6.66] The true discount on a certain sum of money due 3 years hence is dollar 200 and the simple interest

For Competitive Exams

The true discount on a certain sum of money due 3 years hence is dollar 200 and the simple interest on the same sum for the same time and at the same rate is dollar 240. Find the sum and the rate per cent.

6.66

Explanation:

Given that,
True discount = dollar 200
Simple interest = dollar 240
Time = 3 years
Consider,
Sum due=$\dfrac{(S.I.) \times (T.D.)}{(S.I.) - (T.D.)}$
=>Sum due=$\dfrac{(240) \times (200)}{(240) - (200)}$
⇒ Sum due = dollar. 1200
Now,
Rate = $\dfrac{(100) \times (S.I.)}{(Sum due ) \times (T)}$
⇒ Rate = $\dfrac{(100) \times (240)}{(1200 ) \times (3)}$
⇒ Rate = $\dfrac{24000}{3600}$
⇒ Rate = 6.66 %
Therefore, Sum due = dollar. 1200 and Rate = 6.66 %

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