Divide ₹ 8840 between A and B so that the amount received by A at the end of 8 years may be equal to the amount received by B at the end of 10 years, compound interest being at 10\% per annum.
(a)₹ 4640, ₹ 4200
(b)₹ 4840, ₹ 4000
(c)₹ 5000, ₹ 3840
(d)₹ 5240, ₹ 3600
Answer
Answer (as printed): B
Explanation
Let $A^{\prime} s$ share $=₹ x$ and $B^{\prime} s$ share $=₹(8840-x)$. $$\begin{aligned} & \therefore x\left(1+\frac{10}{100}\right)^{8}=(8840-x)\left(1+\frac{10}{100}\right)^{10} \\ & \Rightarrow x=(8840-x)\left(1+\frac{10}{100}\right)^{2} \\ & \Rightarrow x=\frac{121}{100}(8840-x) \\ & \Rightarrow 221 x=121 \times 8840 \\ & \Rightarrow x=\left(\frac{121 \times 8840}{221}\right)=4840 . \end{aligned}$$ Hence, the two parts are ₹ 4840 and ₹ 4000.
Explanation as extracted from the printed page; notation may be imperfect.