CAT 2020

Slot 2

QA

Question & Solution

1. Concept Used

• Topic: Simple Interest vs Compound Interest
• Formula: $$CI_{2yr} = P \cdot \frac{R_1}{100} + P \cdot \frac{R_1}{100} \cdot \left(1 + \frac{R_1}{100}\right), \quad SI_{3yr} = \frac{3 \cdot P \cdot R_2}{100}$$

2. Calculation

Let the principal amount be $$P$$. The compound interest rate is $$R_1 = 5%$$ per annum for 2 years, and the simple interest rate is $$R_2 = 3%$$ per annum for 3 years.

Step 1: Compute Compound Interest for 2 years at 5%.

The CI earned in Year 1 is $$\frac{5P}{100} = 0.05P$$.

The CI earned in Year 2 is $$0.05P \times (1 + 0.05) = 0.05P \times 1.05 = 0.0525P$$.

So, total $$CI = 0.05P + 0.0525P = 0.1025P = \frac{10.25P}{100}$$.

Step 2: Compute Simple Interest for 3 years at 3%.

$$SI = \frac{P \times 3 \times 3}{100} = \frac{9P}{100}$$

Step 3: Set up the equation using the given condition.

$$CI - SI = 1125$$

$$\frac{10.25P}{100} - \frac{9P}{100} = 1125$$

$$\frac{1.25P}{100} = 1125$$

$$1.25P = 112500$$

$$P = \frac{112500}{1.25} = 90000$$

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3. Solution

Answer = 90000 ✅

The principal amount is Rs. 90,000.