CAT 2019

Slot 1

QA

Question & Solution

1. Concept Used

• Topic: Ratio and Proportion — Simple Interest Income
• Formula: $$\text{Interest Income} = \text{Principal} \times \frac{\text{Rate}}{100}$$

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2. Calculation

Let the investments of Amala, Bina, and Gouri be (3k), (4k), and (5k) respectively, and their annual interest rates be (6r), (5r), and (4r) respectively.

The interest income for each person is calculated as (\text{Principal} \times \text{Rate}) (we can absorb the (\frac{1}{100}) factor into the constant):

$$\text{Amala's Interest} = 3k \times 6r = 18kr$$

$$\text{Bina's Interest} = 4k \times 5r = 20kr$$

$$\text{Gouri's Interest} = 5k \times 4r = 20kr$$

Now applying the given condition that Bina's interest exceeds Amala's by Rs 250:

$$20kr - 18kr = 250$$

$$2kr = 250 \implies kr = 125$$

Now the total interest income of all three is:

$$\text{Total} = 18kr + 20kr + 20kr = 58kr$$

$$\text{Total} = 58 \times 125 = \mathbf{7250}$$

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3. Solution

Answer = Option D ✅

The total interest income after one year is Rs 7250.