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CAT 2019 Slot 1 — QA Question 18

Percentage ChangeEasy

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

Answer & solution

  • 31

  • B

    29

  • C

    28

  • D

    32

Solution

Easy

Pin Amala's income against both others: 20%20\% more than Bimala and 20%20\% less than Kamala. This fixes the ratio K:BK:B. Pick convenient numbers, apply the −4%-4\% and +10%+10\% changes, then compute how far new Kamala exceeds new Bimala.

1

Relate the incomes. Amala aa, Bimala bb, Kamala kk.

a=1.2 b=65b(20% more than Bimala)a=0.8 k=45k(20% less than Kamala)⇒ 65b=45k ⇒ kb=32\begin{aligned} &a=1.2\,b=\tfrac{6}{5}b\quad\text{(20\% more than Bimala)}\\ &a=0.8\,k=\tfrac{4}{5}k\quad\text{(20\% less than Kamala)}\\ &\Rightarrow\ \tfrac{6}{5}b=\tfrac{4}{5}k\ \Rightarrow\ \frac{k}{b}=\frac{3}{2} \end{aligned}
2

Choose convenient values. Use the ratio k:b=3:2k:b=3:2.

k=300,b=200\begin{aligned} &k=300,\quad b=200 \end{aligned}
3

Apply the changes. Kamala −4%-4\%, Bimala +10%+10\%.

k′=300×0.96=288b′=200×1.10=220\begin{aligned} &k'=300\times0.96=288\\ &b'=200\times1.10=220 \end{aligned}
4

Percentage excess. How much k′k' exceeds b′b', relative to b′b'.

288−220220×100=68220×100⇒ ≈30.9%≈31%\begin{aligned} &\frac{288-220}{220}\times100=\frac{68}{220}\times100\\ &\Rightarrow\ \approx 30.9\%\approx 31\% \end{aligned}
Excess≈31%\text{Excess}\approx 31\%
CAT 2019 Slot 1 QA Q18: The income of Amala is 20% more than that of Bimala and 20% less than that of Kamala. If Kamala's income goes — Solution | TheCATExam