A sum of ₹ 1550 was lent partly at 5\% and partly at 8\% p.a. simple interest. The total interest received after 3 years was ₹ 300. The ratio of the money lent at 5\% to that lent at 8\% is :
(a)5 : 8
(b)8 : 5
(c)16 : 15
(d)31 : 6
Answer
Answer (as printed): C
Explanation
Let the sum lent at 5\% be ₹ $x$ and that lent at 8\% be $₹(1550-x)$. Then, $$\left(\frac{x \times 5 \times 3}{100}\right)+\left[\frac{(1550-x) \times 8 \times 3}{100}\right]=300$$ $\Leftrightarrow \quad 15 x-24 x+(1550 \times 24)=30000$ $\Leftrightarrow \quad 9 x=7200 \Leftrightarrow x=800$. ∴ Required ratio $=800: 750=16: 15$.
Explanation as extracted from the printed page; notation may be imperfect.