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

Correct Option: 1 (31)

Let the income of Bimala be $B$, Amala be $A$, and Kamala be $K$.

According to the problem:
1. Amala's income is 20% more than Bimala's:

$A=1.20B$

$A=0.80K$

Equating the two expressions for $A$:

$1.20B=0.80K\Rightarrow K=\frac{1.20}{0.80}$

Let's choose a convenient value for Bimala's income, say $B=100$:
Then, Amala's income $A=120$, and Kamala's income $K=150$.

Now we apply the changes:
1. Kamala's income goes down by 4%:

$K_{\text{new}}=150\times (1-0.04)=150\times 0.96=144$

We need to find the percentage by which Kamala's new income exceeds Bimala's new income:

$\text{Percentage Exceed}=\frac{K_{\text{new}}-B_{\text{new}}}{B_{\text{new}}}\times 100$

$\text{Percentage Exceed}=\frac{144-110}{110}\times 100=\frac{34}{110}\times 100\approx 30.91\%$

The value nearest to 30.91% is 31%.