A sum of ₹ 2600 is lent out in two parts in such a way that the interest on one part at 10\% for 5 years is equal to that on another at 9\% for 6 years. The sum lent out at 10\% is :
(a)₹ 1150
(b)₹ 1250
(c)₹ 1350
(d)₹ 1450
Answer
Answer (as printed): C
Explanation
Let the sum lent at 10\% be ₹ $x$ and that lent at 9\% be $₹(2600-x)$. Then, $$\left(\frac{x \times 10 \times 5}{100}\right)=\frac{(2600-x) \times 9 \times 6}{100}$$ $\Leftrightarrow 50 x=(2600 \times 54)-54 x$ $\Rightarrow \quad x=\left(\frac{2600 \times 54}{104}\right)=1350$. ∴ Sum lent at $10 \%=₹ 1350$.
Explanation as extracted from the printed page; notation may be imperfect.