Alex invested his savings in two parts. The simple interest earned on the first part at $15 \%$ per annum for $4$ years is the same as the simple interest earned on the second part at $12 \%$ per annum for $3$ years. Then, the percentage of his savings invested in the first part is

$62.5 \%$

$40 \%$

$60 \%$

$37.5 \%$

✅ Correct Option: 4

Alex splits his savings into two parts and invests them at different interest rates. We need to find what percentage of his total savings went into the first part.

Key insight: When the simple interest earned from both parts is equal, we can find the ratio of the investments.

Let's say:

First part = $x$

Second part = $y$

Simple Interest Formula: $SI = \dfrac{P \times R \times T}{100}$

Where P = Principal, R = Rate%, T = Time in years

The simple interest from both parts is equal:

First part: $SI_1 = \dfrac{x \times 15 \times 4}{100} = \dfrac{60x}{100}$

Second part: $SI_2 = \dfrac{y \times 12 \times 3}{100} = \dfrac{36y}{100}$

Since $SI_1 = SI_2$ :

$\dfrac{60x}{100} = \dfrac{36y}{100}$

We cancel out the common factor of 100:

$60x = 36y$

We divide both sides by 12 to simplify:

$5x = 3y$

Finding the ratio: $\dfrac{x}{y} = \dfrac{3}{5}$

If $x : y = 3 : 5$ , then:

First part = 3 units

Second part = 5 units

Total savings = 3 + 5 = 8 units

Percentage of first part:

$\dfrac{\text{First part}}{\text{Total savings}} \times 100 = \dfrac{3}{8} \times 100 = 37.5\%$

Therefore, 37.5% of his savings was invested in the first part.

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Alex invested his savings in two parts. The simple interest earned on the first part at $15 \%$ per annum for $4$ years is the same as the simple interest earned on the second part at $12 \%$ per annum for $3$ years. Then, the percentage of his savings invested in the first part is