Question : At some rate of Simple interest, A lent Rs. 6,000 to B for 2 years and Rs. 1,500 to C for 4 years and received 900 as interest from both of them together. The Rate of interest per annum was:
Option 1: 5%
Option 2: 6%
Option 3: 8%
Option 4: 10%
Correct Answer: 5%
Solution :
First sum, $P_1$ = Rs. 6,000
First term, $n_1$ = 2 years
Second sum, $P_2$ = Rs. 1,500
Second term, $n_2$ = 4 years
Interest, SI = Rs. 900
Let $R$ be the rate.
We know, Simple interest = $\frac{\text{Principal × Rate × Time}}{100}$
According to the question,
$900 = \frac{6000×2×R}{100}+\frac{1500×4×R}{100}$
$⇒ 900 = 180R$
$\therefore R= 5\%$
Hence, the correct answer is 5%.
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