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CAT 2024 Slot 3 QA Question 5

Multiple choice (+3 / −1) · Arithmetic · Ratio, Proportion & Variation · Try it, then check the answer and solution below.

CAT 2024 Slot 3QAArithmetic • Ratio, Proportion & VariationEasy
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.Ifthetotalcultivationareaofwheatandmustardareintheratio. If the total cultivation area of wheat and mustard are in the ratio11: 9 , then the ratio of cultivation area of wheat and mustard in the land owned by Rajesh is
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Answer and solution

Answer: D) 7:9

📌 Core Concept
The problem involves ratios and proportions. We use the concept of alligation or system of equations to solve for unknown ratios.
🔢 Step-by-Step Solution
1
Given Data:
Rajesh's land: 20 hectares
Vimal's land: 30 hectares
Ratio of wheat to mustard in Vimal's land: 5:35:3
Total ratio of wheat to mustard in both lands: 11:911:9
2
Calculate Wheat and Mustard in Vimal's Land:
Total parts in Vimal's land = 5 + 3 = 8$
Each part = 308\frac{30}{8} = 3.75$ hectares
Wheat in Vimal's land = 5 × 3.75 = 18.75$ hectares
Mustard in Vimal's land = 3 × 3.75 = 11.25$ hectares
3
Let Total Wheat and Mustard Be 11k11k and 9k9k Respectively:
Total wheat = 11k$
Total mustard = 9k$
4
Express Rajesh's Wheat and Mustard:
Rajesh's wheat = 11k - 18.75$
Rajesh's mustard = 9k - 11.25$
5
Sum of Rajesh's Wheat and Mustard Equals His Total Land:
(11k−18.75)+(9k−11.25)=20(11k - 18.75) + (9k - 11.25) = 20 20k−30=2020k - 30 = 20 20k=50  ⟹  k=2.520k = 50 \implies k = 2.5
6
Calculate Rajesh's Wheat and Mustard:
Wheat = 11 × 2.5 - 18.75 = 27.5 - 18.75 = 8.75$ hectares
Mustard = 9 × 2.5 - 11.25 = 22.5 - 11.25 = 11.25$ hectares
7
Find the Ratio of Wheat to Mustard in Rajesh's Land:
8.7511.25=79\frac{8.75}{11.25} = \frac{7}{9}
⚡ 30-Second Shortcut
Use the concept of ratios and set up equations based on total areas.
Recognize that the ratio 11:911:9 is the combined ratio, so subtract Vimal's share to find Rajesh's share.
🎯 Final Answer
Correct Answer: Option D

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