What sum of money invested at 7.5% p.a.,simple interest for 2 years produces twice as much as Rs.9600 in 3 years 6 months at 10% p.a. interest?

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Solution

$CASE 1 : Principal, P_{1} = Rs 9600 Rate, R_{1} = 10 % p . a Time, T_{1} = 3 yrs 6 months = 3 \frac{1}{2} yrs = \frac{7}{2} yrs Now, Interest, I_{1} = \frac{P_{1} R_{1} T_{1}}{100} = \frac{9600 \times 10 \times 7}{200} = Rs 3360 CASE 2 : Let the required sum = Rs P Rate, R = 7.5 % p . a . = \frac{15}{2} % p . a . Time, T = 2 yrs Now, Interest, I = \frac{PRT}{100} \Rightarrow 2 I_{1} = \frac{P \times 15 \times 2}{200} \Rightarrow 3360 = \frac{15 P}{200} \Rightarrow P = 44800 So, required sum = Rs 44, 800$

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