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A certain sum of money amounts to $Rs . 6300$ in 2 years $Rs . 7875$ in 3 years and 9 months at simple interest. Find the rate of interest per annum.

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30 %

50 %

20 %

40 %

answer is C.

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Detailed Solution

Let the principle = Rs.P and Rate of interest = R%.
Amount

(A) = P (1 + \frac{TR}{100})

From the question we have,

Rs . 6300 = P (1 + \frac{2 R}{100}) \dots \dots \dots \dots . . (1)

Rs . 7875 = P (1 + \frac{15 R}{400}) \dots \dots \dots \dots

(2)

∵ T = 3 \frac{9}{12} = \frac{15}{4}

years

Now dividing (1) by (2) we get,

\frac{6300}{7375} = \frac{P (1 + \frac{2 \times R}{100})}{P (1 + \frac{15 \times R}{400})}

\frac{4}{5} = \frac{(100 + 2 R) 400}{(400 + 15 R) 100}

\frac{4}{5} = \frac{(100 + 2 R) 4}{(400 + 15 R)}

400 + 15 R = 500 + 10 R

15 R - 10 R = 500 - 100

5 R = 400

R = 20 %

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