Question

If 12 labourers take 70 days to complete one task, how many days will 21 labourers take to complete the same task?

Answer 1

12 labourers take 70 days to complete one task.
Let 21 labourers take x days to complete the task.
The given information can be represented in the following table:

Days : x	70	x
Number of labourers : y	12	21

Here number of labourers and days taken by them to complete one task are in indirect proportion because number of days taken by labourers will decrease with an increase in the number of labourers. In indirect variation,the product of the number of labourers and the number of days taken by them will remain constant.
∴ x₁y₁ = x₂y₂
∴ 70 × 12 = x × 21
∴ $x=\frac{70\times 12}{21}$= 40 days.
∴ 21 labourers will take 40 days to complete the task.