The area of cultivated land and the crop harvested is a case of direct proportion. State whether the statement is true (T) or false (F)

Solution:

The statement is True.

The more the area is cultivated the more the yield of the crop will be. In other words the more the area cultivated the more the crop will be harvested. This is a direct variation.

Mathematically stated we have:

Crop Harvested(C) ∝ Area under cultivation(A)

C ∝ A

C/A = k = constant of proportionality

✦ Try This: Two large fields adjacent to each other have 15 hectares and 30 acres are equally fertile with a yield of 20 quintals per hectare. Find the crop harvested from the two fields in quintals.

In the given problem statement the yield is the constant of proportionality between Crop harvested and area of land.

C = kA

k = 20 quintals/hectare

a) Amount of Crop from 15 hectares of land:

C = 20 × 15 = 300 quintals

b) Amount of crop from 30 hectares of land

C = 20 × 30 = 600 quintals

Hence as the area increases the quantity of crop harvested also increases as evident from the above calculations.

☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 13

NCERT Exemplar Class 8 Maths Chapter 10 Problem 59

The area of cultivated land and the crop harvested is a case of direct proportion. State whether the statement is true (T) or false (F)

Summary:

The area of cultivated land and the crop harvested is a case of direct proportion. The statement is True

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