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Ratio of Daily Earnings

CAT 2021 Slot 2 · Quantitative Ability · Medium · Ratios & Proportions

This is a medium Quantitative Ability question from the CAT 2021 Slot 2 paper. It tests Ratios & Proportions. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

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The amount Neeta and Geeta together earn in a day equals what Sita alone earns in 6 days. The amount Sita and Neeta together earn in a day equals what Geeta alone earns in 2 days. The ratio of the daily earnings of the one who earns the most to that of the one who earns the least is

  1. A.

    7 : 3

  2. B.

    11 : 3

  3. C.

    11 : 7

  4. D.

    3 : 2

Answer

B

Explanation

Let N,G,SN, G, S be the daily earnings of Neeta, Geeta, and Sita respectively.

Given equations:

  1. N+G=6SN + G = 6S
  2. S+N=2G  ⟹  N=2G−SS + N = 2G \implies N = 2G - S

Substitute N=2G−SN = 2G - S into equation 1: (2G−S)+G=6S  ⟹  3G=7S  ⟹  G=73S(2G - S) + G = 6S \implies 3G = 7S \implies G = \frac{7}{3}S

Now find NN in terms of SS: N=2(73S)−S=143S−S=113SN = 2\left(\frac{7}{3}S\right) - S = \frac{14}{3}S - S = \frac{11}{3}S

So S:G:N=1:73:113=3:7:11S : G : N = 1 : \frac{7}{3} : \frac{11}{3} = 3 : 7 : 11. Most earner = Neeta (11), Least earner = Sita (3). Ratio =11:3= 11 : 3.

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