QUESTION

# 12 workers can complete a piece of work in 10 days. If the number of workers is reduced to $\dfrac{1}{3}$rd of the original number, then how many more days would be required to complete the same work?${\text{A}}{\text{.}}$ 3${\text{B}}{\text{.}}$ 5${\text{C}}{\text{.}}$ 15${\text{D}}{\text{.}}$ 20

Hint: If the number of workers is reduced to $\dfrac{1}{3}$rd, then the number of days required to complete the same work will increase by 3 times [since, Work Done = Workforce$\times$ Time].

Also, that the number of workers is reduced to $\dfrac{1}{3}$.
Now, $\dfrac{1}{3}$rd of original no. of workers $= \dfrac{1}{3} \times 12 = 4$.
Therefore, 4 workers can complete the same work in $\dfrac{{12 \times 10}}{4} = \dfrac{{120}}{4} = 30$ (Because work remains same)
Hence, the number of extra days that will be required by a smaller number of workforces will be $= (30 - 10) = 20$.