If the work done by x men I (x + 1) days is equal to the work done by (x + 5) men in (x - 2) days, then what is the value of x ?

Correct option is A

Given:

The work done by x men in (x + 1) days = The work done by (x + 5) men in (x - 2) days

Solution:

Let W denote the work done by one man in one day.

The total work done by x men in (x + 1) days is W × X × (x + 1).

The total work done by (x + 5) men in (x - 2) days is: W × (x + 5) × (x - 2).

According to the problem, these two amounts of work are equal:

W × x × (x + 1) = W × (x + 5) × (x - 2)

=> x × (x + 1) = (x + 5) × (x - 2)

=> x²+ x =x²- 2x + 5x - 10

=> x = 3x - 10

=> 2x = 10

=> x = 5

∴ The correct answer is 5.