CAT 2019 Quant Question with Solution 2

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

  1. 31
  2. 28
  3. 32
  4. 29
Show Answer

Correct Answer: Option: 1

Let the income of Bimla be Rs. 100

Amla’s income = 1.2*100 = Rs. 120

Also, Amla’s income = $\frac{4}{5}\times$ Kamla’s income

Therefore, Kamla’s income = $\frac{5}{4}\times 120$=Rs. 150

 Kamala's new income with 4% decrease = 0.96×150 =Rs. 144

Bimla’s new income with 10% increase = 1.1×100= Rs. 110

Required percentage increase = $\left( \frac{144-110}{110} \right)\times 100\approx 31%$


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