CAT 2022

Slot 1

QA

Question & Solution

1. Concept Used

• Topic: Simple Interest & Ratio/Proportion
• Formula: $$SI = \frac{P \times R \times T}{100}$$

2. Calculation

Let the amount invested in the first part be $x$ and in the second part be $y$, so total savings = $x + y$.

The simple interest on the first part at 15% per annum for 4 years is: $$SI_1 = \frac{x \times 15 \times 4}{100} = \frac{60x}{100}$$

The simple interest on the second part at 12% per annum for 3 years is: $$SI_2 = \frac{y \times 12 \times 3}{100} = \frac{36y}{100}$$

Since $SI_1 = SI_2$, we equate them: $$\frac{60x}{100} = \frac{36y}{100}$$ $$60x = 36y$$ $$5x = 3y \implies y = \frac{5x}{3}$$

Now, the percentage of savings invested in the first part: $$\text{Required %} = \frac{x}{x + y} \times 100$$

Substituting $y = \frac{5x}{3}$: $$= \frac{x}{x + \frac{5x}{3}} \times 100 = \frac{x}{\frac{3x + 5x}{3}} \times 100 = \frac{x}{\frac{8x}{3}} \times 100 = \frac{3}{8} \times 100 = 37.5%$$

Key Insight: The ratio $x : y = 3 : 5$, meaning out of every 8 parts of total savings, only 3 parts are in the first investment. This is why the first part, despite having a higher interest rate (15%), holds a smaller share — it compensates through a longer time period.

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3. Solution

Answer = Option A ✅

The final calculated value is 37.5% of his total savings was invested in the first part.