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Ratio of crop land distribution

CAT 2024 Slot 3 · Quantitative Ability · Easy · Arithmetic

This is an easy Quantitative Ability question from the CAT 2024 Slot 3 paper. It tests Arithmetic. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

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Rajesh and Vimal own 20 hectares and 30 hectares of agricultural land, respectively, which are entirely covered by wheat and mustard crops. The cultivation area of wheat and mustard in the land owned by Vimal are in the ratio of 5 : 3. If the total cultivation area of wheat and mustard are in the ratio 11 : 9, then the ratio of cultivation area of wheat and mustard in the land owned by Rajesh is

  1. A.

    1 : 1

  2. B.

    7 : 9

  3. C.

    4 : 3

  4. D.

    3 : 7

Answer

B

Explanation

Total land = 20+30=5020 + 30 = 50 hectares.

Total wheat area = 1120×50=27.5\frac{11}{20} \times 50 = 27.5 hectares. Total mustard area = 920×50=22.5\frac{9}{20} \times 50 = 22.5 hectares.

For Vimal (30 hectares, ratio 5 : 3):

  • Wheat =58×30=18.75= \frac{5}{8} \times 30 = 18.75 hectares
  • Mustard =38×30=11.25= \frac{3}{8} \times 30 = 11.25 hectares

For Rajesh:

  • Wheat =27.5−18.75=8.75= 27.5 - 18.75 = 8.75 hectares
  • Mustard =22.5−11.25=11.25= 22.5 - 11.25 = 11.25 hectares

Ratio of wheat to mustard for Rajesh =8.75:11.25=7:9= 8.75 : 11.25 = 7 : 9.

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