Averages , Ratio and Proportion Question 8 - 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
- Find the total absolute crop areas:
Total aggregate land pool = 20 + 30 = 50 hectares.
The overall total ratio of Wheat to Mustard is 11 : 9.
Total Wheat Area = 11/20 × 50 = 27.5 hectares
Total Mustard Area = 9/20 × 50 = 22.5 hectares
- Isolate Vimal's crop layout:
Vimal owns 30 hectares, split in a 5 : 3 ratio:
Vimal's Wheat Area = 5/8 × 30 = 18.75 hectares
Vimal's Mustard Area = 3/8 × 30 = 11.25 hectares
- Calculate Rajesh's layout via subtraction:
Rajesh's Wheat Area = 27.5 − 18.75 = 8.75 hectares
Rajesh's Mustard Area = 22.5 − 11.25 = 11.25 hectares
Rajesh's Crop Ratio (Wheat : Mustard) = 8.75 : 11.25 = 7 : 9
Correct Option: B
💡 FundaMakers Tip:
Do not carry complex fraction expressions like k/(k + 1) through your calculation. Find the absolute total areas across the combined 50-hectare pool first. Subtracting Vimal's land share from these totals leaves you with Rajesh's breakdown directly, keeping the final ratio step clean.