Question : Two equal sums are lent at 10% and 8% simple interest p.a. respectively, at the same time. The first sum was received 2 years earlier than the second one and the amount received in each case was INR 36,900. Each sum was ______.
Option 1: INR 20,500
Option 2: INR 20,200
Option 3: INR 18,100
Option 4: INR 21,500
Correct Answer: INR 20,500
Solution : Given : $R_1$ = 10% $R_2$ = 8% $A$ = INR 36900 Let the year be $t$ years and the principal be $P$ According to the question, $\Rightarrow (t + 2)\times 8 = t\times 10$ $\Rightarrow 8t + 16 = 10t$ $\Rightarrow 2t = 16$ $\Rightarrow t = \frac{16}{2} = 8$ Again $A = P(1 + \frac{rt}{100})$ $\Rightarrow 36900 = P(1 + \frac{8\times 10}{100})$ $\Rightarrow 36900 = P + 0.8P$ $\Rightarrow 1.8P = 36900$ $\Rightarrow P = 20,500$ Hence, the correct answer is INR 20,500.
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