QQuestion
If 15 farmers can cultivate 18 bighas of land in 5 days, determine by using the theory of variation the number of days required by 10 farmers to cultivate 12 bighas of land.
✓Answer
No. of farmers = A, no. of days = B & area of land = C
No. of days is in inverse variation with no. of farmers, when area of land remains constant
i.e., B ∝ \frac{1}{A} when C is constant
Again, No. of days is indirect variation with area of land; when No. of farmers remains constant
∴ B ∝ C when A is Constant.
According to the theorem on joint variation,
B ∝ \frac{C}{A} when C & A both vary
∴ B = K \frac{C}{A} where K is a constant of variation.
Given A = 15, B = 5, & C = 18.
5 = K \frac{18}{15}
or, K = \frac{15 \times 5}{18} = \frac{25}{6}
⇒ B = K \frac{C}{A}
⇒ B = \frac{25}{6} \times \frac{12}{10} = 5
∴ No. of days = 5.
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