The simple interest on a certain sum for $5 y e a r s$ at $8 % p . a .$ is $R s 200$ less than the simple interest on the same sum for $3 y e a r s$ and $4 m o n t h s$ at $18 % p . a .$ find the sum.

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Solution

Let the principal be Rs $P$ .
$R_{1} = 18 % p . a . T_{1} = 3 y e a r s 4 m o n t h s = 3 \frac{4}{12} Y = 3 \frac{1}{3} Y = \frac{10}{3} Y R_{2} = 8 % p . a . T_{2} = 5 y e a r s D i f f e r e n c e o f S I = R s 200 \frac{P \times R_{1} \times T_{1}}{100} - \frac{P \times R_{2} \times T_{2}}{100} = 200 \frac{P \times 18 \times 10}{100 \times 3} - \frac{P \times 8 \times 5}{100} = 200 \frac{60 P}{100} - \frac{40 P}{100} = 200 \frac{20 P}{100} = 200 P = \frac{200 \times 100}{20} = R s 1000$

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