A man invests a certain sum of money at 6\% p.a. simple interest and another sum at 7\% p.a. simple interest. His income from interest after 2 years was ₹ 354. One-fourth of the first sum is equal to onefifth of the second sum. The total sum invested was:
(a)₹ 2600
(b)₹ 2700
(c)₹ 2880
(d)₹ 2900
Answer
Answer (as printed): B
Explanation
Let the sums be $x$ and $y$. $$\frac{x \times 6 \times 2}{100}+\frac{y \times 7 \times 2}{100}=354 \text { or } 6 x+7 y=17700 .$$ Also, $\frac{x}{4}=\frac{y}{5}$ or $5 x-4 y=0$ Solving (i) and (ii), we get : $x=1200$ and $y=1500$. ∴ Total sum = ₹ 2700.
Explanation as extracted from the printed page; notation may be imperfect.