CAT 2019 Slot 1 QA Question & Solution
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
Options
Solution
Assume Bimla’s income $= 100a$.
Then Amala’s income $= 120a$.
Kamala’s income $= 120a \times \frac{100}{80} = 150a$.
If Kamala’s income decreases by $4%$:
$$
\text{New Kamala income} = 150a - 150a \left( \frac{4}{100} \right)
= 150a - 6a = 144a
$$
If Bimla’s income increases by $10%$:
$$
\text{New Bimla income} = 100a + 100a \left( \frac{10}{100} \right)
= 110a
$$
Difference between Kamala and Bimla (percentage by which Kamala exceeds Bimla):
$$
\frac{144a - 110a}{110a} \times 100
= \frac{34a}{110a} \times 100
= 31
$$
Kamala’s income exceeds Bimla’s income by 31%.