Question

If 15 men can do a piece of work in 20 days. In how many days can 25 men finish the same work?
(a) 12
(b) 15
(c) 2
(d) 20

Answer 1

Hint: We start solving the problem by assigning the variables for the piece of work and part of the work done by each man in a day. We then find the total amount of work done by multiplying the number of days and a total number of men to the part of work done in each day by each man and equate it to a piece of work. We then make the necessary calculations to get the part of work done by each man in one day. We then multiply this result by 25 to get the amount of work done by 25 men each day. We then total the amount of work with this result to get the required result.

Complete step by step answer:
According to the problem, we are given that 15 men can do a piece of work in 20 days. We need to find the number of days that this work can be finished by 25 men.
Let us assume the piece of work be ‘x’ and the part of the work done by each man per day be ‘y’.
Let us now find the amount of work done by 15 men in a single day, which is $ 15\times y=15y $
So, we have $ 20\times 15y=x $ .
 $ \Rightarrow 300y=x $ .
 $ \Rightarrow y=\dfrac{x}{300} $ .
Now, let us find the amount of work done by 25 men in a single day.
We get $ 25\times y=25\times \dfrac{x}{300}=\dfrac{x}{12} $ .
Now, let us assume the number of days required for 25 men to finish the work be ‘n’.
So, we get $ n\times \dfrac{x}{12}=x $ .
 $ \Rightarrow n=12 $ .
So, we have found the number of days required for 25 men to finish the work as 12 days.
 $ \therefore, $ The correct option for the given problem is (a).

Note:
We can also solve the problem as shown below:
Let us assume the work done by each man in a single day is 1 unit. Then the total amount of work done by 15 men in 20 days will be $ 15\times 20\times 1=300 $ units.
Now, we need to find the number of days required for 25 men to finish 300 units of work. Let it be ‘n’.
So, we get $ 25\times n=300\Leftrightarrow n=12 $ days.