Sriram invested equal sums of money in two schemes. Under scheme $X$, the compound interest rate was 10 p.c.p.a. and under scheme $Y$, the compound interest rate was 12 p.c.p.a. The interest after 2 years on the sum invested in scheme $X$ was ₹ 63 . How much is the interest earned under scheme $Y$ after 2 years?
(a)₹ 70.56
(b)₹ 76.32
(c)₹ 79.0272
(d)₹ Cannot be determined
(e)None of these
Answer
Answer (as printed): B
Explanation
Let each sum be ₹ P. Then, $$\begin{aligned} & P\left(1+\frac{10}{100}\right)^{2}-P=63 \\ & \Rightarrow\left(P \times \frac{11}{10} \times \frac{11}{10}\right)-P=63 \\ & \Rightarrow \frac{121}{100} P-P=63 \\ & \Rightarrow \frac{21}{100} P=63 \\ & \Rightarrow P=\left(\frac{63 \times 100}{21}\right)=300 . \end{aligned}$$ Hence, C.I. $=₹\left[300\left(1+\frac{12}{100}\right)^{2}-300\right]$ $$=₹\left[\left(300 \times \frac{28}{25} \times \frac{28}{25}\right)-300\right]=₹ 76.32 .$$
Explanation as extracted from the printed page; notation may be imperfect.