Average, Mixture and Alligation Question 5 - CAT 2024
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:
Step-by-Step Explanation
- Analyze the Global Totals:
Total land area = 20 hectares (Rajesh) + 30 hectares (Vimal) = 50 hectares.
The total cultivation area ratio of wheat to mustard is 11 : 9.
Total Wheat Area = 11 / (11 + 9) × 50 = 11 / 20 × 50 = 27.5 hectares
Total Mustard Area = 50 − 27.5 = 22.5 hectares
- Analyze Vimal's Sub-allocations:
Vimal owns 30 hectares, split in a 5 : 3 ratio between wheat and mustard.
Vimal's Wheat Area = 5 / 8 × 30 = 18.75 hectares
Vimal's Mustard Area = 30 − 18.75 = 11.25 hectares
- Isolate Rajesh's Sub-allocations:
Rajesh's Wheat Area = Total Wheat − Vimal's Wheat = 27.5 − 18.75 = 8.75 hectares
Rajesh's Mustard Area = Total Mustard − Vimal's Mustard = 22.5 − 11.25 = 11.25 hectares
- Determine Rajesh's Ratio:
Ratio = 8.75 : 11.25 = 875 : 1125
Dividing both values by their greatest common divisor (125):
Ratio = 7 : 9
Correct Option: B
💡 FundaMakers Tip:
When handling weighted average problems involving clean absolute totals (like 20, 30, and 50 hectares), compute the real component weights directly rather than setting up fractional mixing equations. Working with simple numbers like 27.5 and 18.75 keeps your steps intuitive and avoids errors with cross-multiplication.