It is good farming practice to apply 10 tonnes of cow manure for 1 acre of land. A farmer is planning to grow tomatoes in a plot of size 200 ft by 500 ft. How much manure should he buy? (Please refer to the section on Unit Conversions earlier in this chapter).

Question

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We have 1 ton = 1,000 kg
∴ 10 tonnes = 10 × 1,000 = 10,000 kg
Also, 1 acre = 43,560 sq. ft.
∴ Ratio of cow manure to area of land in kg and sq. ft. = 10,000 : 43,560
Size of plot = 200 ft. by 500 ft.
∴ Area of plot = 200 × 500 = 1,00,000 sq. ft.
Let cow manure be x kg.
∴ Ratio of cow manure to area of plot = x : 1,00,000
These ratios are in proportion.
∴ 10,000 : 43,560 :: x : 1,00,000
⇒ $\frac{10,000}{43,560}=\frac{x}{1,00,000}$
⇒ 43,560x = 10,000 × 1,00,000 = 1,00,00,00,000
⇒ x = $\frac {1,00,00,00,000}{43,560}$
⇒ x = 22956.84
∴ Required cow manure = 22956.84 kg = 22.95684 tonnes.

Proportional Reasoning 1 — Question 8