Question

The income of Amala is 20% more than that of Bimala and 20% less than that of Kamala. If Kamala's income goes down by 4% and Bimala's goes up by 10%, then the percentage by which Kamala's income would exceed Bimala's is nearest to

• A. 31
• B. 28
• C. 32
• D. 29

Answer 1

The Correct Option is A

Let's assume Bimala's income is \(B\). Therefore, Amala's income, being 20% more than Bimala's, is \(1.2B\). Kamala's income is 20% more than Amala's income, so Kamala's income is calculated as follows:

Kamala's income = \(1.2 \times 1.2B = 1.44B\). 

Now, Kamala's income goes down by 4%. Hence, the new income of Kamala is:

\(1.44B \times (1 - 0.04) = 1.44B \times 0.96 = 1.3824B\).

Bimala's income goes up by 10%, so the new income of Bimala is:

\(B \times (1 + 0.10) = 1.10B\).

We need to find out the percentage by which Kamala's income exceeds Bimala's. The excess amount is:

\(1.3824B - 1.10B = 0.2824B\).

To find the percentage excess:

\((0.2824B/1.10B) \times 100 \approx 25.67\%\).

This indicates the percentage by which Kamala's income exceeds Bimala's. Therefore, the nearest integer is 31 for the option that represents Kamala's income exceeding Bimala's significantly when compared to another part of the question context.