Percentage problem 6 by Dhaval Furia

Let:

$a = \text{ Amala's Income}$

$b = \text{ Bimala's Income}$

$k = \text{ Kamala's Income}$

And let's use subscripts $1$ and $2$ to refer to the initial and final incomes (example: $a_{1})$

Initial Conditions

The income of Amala is 20% more than that of Bimala. $\rightarrow a_{1} = b_{1}(1.2)$

The income of Amala is 20% less than that of Kamala. $\rightarrow a_{1} = k_{1}(1-0.2)=k_{1}(0.8)$

Combining the two above statements tells us:

$a_{1} = b_{1}(1.2) = k_{1}(0.8)$

or, more simply,

$1.5b_{1}=k_{1}$

Final Conditions

Kamala's income goes down by 4%. $\rightarrow k_{2}=k_{1}(1-0.04)=k_{1}(0.96)$

Bimala's income goes up by 10%. $\rightarrow b_{2}=b_{1}(1+0.10)=b_{1}(1.10)$

Calculations

So we essentially need to find the $k_{2}$ to $b_{2}$ ratio.

From here, just substitute the values to solve for one variable, and then you can find the answer, which ends up being 1.44/1.1=1.31, indicating a 31% increase.