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 Kamalas's income would exceed Bimala's is nearest to

Options

A. 29
B. 32
C. 31
D. 28

Answer

To solve the problem step by step, we will denote the incomes of Bimala, Amala, and Kamala as \( B \), \( A \), and \( K \) respectively.

### Step 1: Establish the relationship between the incomes.
Given that Amala's income is 20% more than Bimala's income, we can express this as:
\[ A = B + 0.2B = 1.2B \]
Also, since Amala's income is 20% less than Kamala's income, we can express this as:
\[ A = K - 0.2K = 0.8K \]

### Step 2: Relate Kamala's income to Bimala's income.
From the two equations we have:
\[ 1.2B = 0.8K \]
To find \( K \) in terms of \( B \), we rearrange the equation:
\[ K = \frac{1.2B}{0.8} = 1.5B \]

### Step 3: Calculate the new incomes after the changes.
Now we will calculate the new incomes after the specified changes:
- Kamala's income decreases by 4%:
\[ K' = K - 0.04K = 0.96K = 0.96 \times 1.5B = 1.44B \]

- Bimala's income increases by 10%:
\[ B' = B + 0.1B = 1.1B \]

### Step 4: Find the difference in incomes.
Now we need to find how much Kamala's new income exceeds Bimala's new income:
\[ \text{Difference} = K' - B' = 1.44B - 1.1B = 0.34B \]

### Step 5: Calculate the percentage by which Kamala's income exceeds Bimala's income.
To find the percentage by which Kamala's income exceeds Bimala's income, we use the formula:
\[ \text{Percentage} = \left(\frac{\text{Difference}}{B'}\right) \times 100 = \left(\frac{0.34B}{1.1B}\right) \times 100 \]
This simplifies to:
\[ \text{Percentage} = \left(\frac{0.34}{1.1}\right) \times 100 \approx 30.91\% \]

### Step 6: Round the percentage.
Rounding 30.91% gives us approximately 31%.

### Final Answer:
Thus, the percentage by which Kamala's income exceeds Bimala's income is approximately **31%**.

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