Arithmetic

Ratio, Proportion & Variation

Easy

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

4:3

3:7

1:1

7:9

✅ Correct Option: 4

Very easy, the question is just written in a confusing way!

We have two farmers:

Rajesh: owns 20 hectares

Vimal: owns 30 hectares

Both grow only wheat and mustard crops on their entire land.

Key Information Given:

Vimal's wheat : mustard ratio = 5 : 3

Total wheat : mustard ratio = 11 : 9

We need to find Rajesh's wheat : mustard ratio

Let's find the exact area used by Vimal for each crop:

Vimal's wheat area = $\tfrac{5}{8} \times 30 = \tfrac{150}{8} = 18.75$ hectares

Vimal's mustard area = $\tfrac{3}{8} \times 30 = \tfrac{90}{8} = 11.25$ hectares

Let's find the exact area of the total for each crop (Total Area - Vimal's Area = Rajesh's Area:

Total wheat area = $\tfrac{11}{20} \times 50 = \tfrac{550}{20} = 27.5$ hectares

Total mustard area = $\tfrac{9}{20} \times 50 = \tfrac{450}{20} = 22.5$ hectares

Rajesh's = Total - Vimal's

Rajesh's wheat area $= 27.5 - 18.75 = 8.75$ hectares

Rajesh's mustard area $= 22.5 - 11.25 = 11.25$ hectares

Check: 8.75 + 11.25 = 20 (This matches Rajesh's total land)

Rajesh's ratio

$= W:M$

$= 8.75 : 11.25$

Simplify decimal ratios:

Multiply by $1000 = 875 : 1125$

Divide by $25 = 35 : 45$

Divide by $5 = 7 : 9$

The ratio of wheat to mustard cultivation on Rajesh's land is 7 : 9.

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