Question

Athul invested his savings in two schemes. The simple interest earned on the first scheme at 15% per annum for 4 years is the same as the simple interest earned on the second scheme at 12% per annum for 3 years. Then, the percentage of his savings invested in the first scheme is

• A. 60
• B. 37.5
• C. 62.5
• D. 40

Answer 1

The Correct Option is B

Let the total savings of Athul be \( S \). Let the amount invested in the first scheme be \( x \) and the amount invested in the second scheme be \( S - x \). The simple interest earned on the first scheme is:
\[ \text{Interest on first scheme} = \frac{x \times 15 \times 4}{100} = \frac{60x}{100} = 0.6x \]
The simple interest earned on the second scheme is:
\[ \text{Interest on second scheme} = \frac{(S - x) \times 12 \times 3}{100} = \frac{36(S - x)}{100} = 0.36(S - x) \]
Since the interests are equal:
\[ 0.6x = 0.36(S - x) \]
Solve the equation:
\[ 0.6x = 0.36S - 0.36x \quad \Rightarrow \quad 0.6x + 0.36x = 0.36S \quad \Rightarrow \quad 0.96x = 0.36S \]
\[ x = \frac{0.36S}{0.96} = 0.375S \]

Therefore, \( x = 37.5\% \) of \( S \).

To solve this type of problem, set up equations for the simple interest and solve for the unknown investment.