Question & Answer
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

ANSWER Verified Verified
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].

Complete step-by-step answer:
We have been given that 12 workers can complete a piece of work in 10 days.
Also, that the number of workers is reduced to $\dfrac{1}{3}$.
We know that if the workforce is reduced then the time will increase.
Now, $\dfrac{1}{3}$rd of original no. of workers $ = \dfrac{1}{3} \times 12 = 4$.
It is a case of inverse variation as we know,
So, 12 workers can complete a work in 10 days
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$.
Hence, the correct option is D.

Note: Whenever such types of questions appear we should remember that work done will remain the same in both cases. So we can equate the work done in both cases. This will give us the right solution.