Two equal sums of money are lent at the same time at 8\% and 7\% per annum simple interest. The former is recovered 6 months earlier than the latter and the amount in each case is ₹ 2560. The sum and the time for which the sums of money are lent out are (M.A.T., 2005)
(a)` 2000, 3.5 years × 4 years
(b)` 1500, 3.5 years × 4 years
(c)` 2000, 4 years × 5.5 years
(d)` 3000, 4 years × 4.5 years
Answer
Answer (as printed): A
Explanation
Let each sum $=₹ x$. Let the first sum be invested for $\left(T-\frac{1}{2}\right)$ years and the second sum for T years. Then, $$x+\frac{x \times 8 \times\left(T-\frac{1}{2}\right)}{100}=2560$$ ⇒ $$100 x+8 x T-4 x=256000$$ ⇒ $$96 x+8 x T=256000$$ And, $$x+\frac{x \times 7 \times T}{100}=2560 \Rightarrow 100 x+7 x T=256000$$ From (i) and (ii), we get: $96 x+8 x T=100 x+7 x T$ ⇒ $$4 x=x T \quad \Rightarrow \quad T=4 .$$ Putting $T=4$ in (i), we get: $96 x+32 x=256000$ ⇒ $$128 x=256000 \Rightarrow x=2000 .$$
Explanation as extracted from the printed page; notation may be imperfect.