Question

18 men can reap a field in 35 days. For reaping the same field in 15 days, how many men are required?

Answer 1

Hint: To find the value of number of men for reaping the field, we will use the unitary method. Where to find the total number of men required, we will first find the number of days taken by one man to reap and divide the product by the total number of days asked in the question i e. 15 days.

Complete step by step solution:

The total number of men required to reap the field in 35 days is 18 men. To find the men required to reap the field in 15 days, we first need to find the total number of days required by one man to reap the field, so we use the unitary method and that is:

If \[18\] men can reap a field in \[35\] days.

Then 1 man can leap a field in \[35\times 18\] days.

If 1 man can reap a field in \[35\times 18\] days, then for \[15\] days the total number of men required is:

The total number of days worked by one man is \[35\times 18\] days and to find the men required we use the values in:

\[\Rightarrow \dfrac{35\times 18}{15}\]

\[\Rightarrow 42\]

Therefore, the total number of men that are working/reaping the field in \[15\] days is \[42\].

Note: Another method to solve the question is by equating the work done together for both 18 days and 15 days and placing them in equal to each other \[15x=35\times 18\] where \[x\] is the unknown number of men working on the field for 15 days.

\[\Rightarrow 15x=35\times 18\]

\[\Rightarrow x=\dfrac{35\times 18}{15}\]

\[\Rightarrow x=42\] men