Explanation:

- To solve the problem, set up an equation based on the work equivalence:

$$x\times (x+1)=(x+5)\times (x-2)$$

- Simplify the equation:

$$x^2+x=x^2+3x-10$$

- Simplify further to find:

$$x=5$$

- Option 1: 5

- This is the correct value of x as calculated above.

- Option 2: 6

- If x = 6, left-hand side does not equal the right-hand side in our equation.

- Option 3: 7

- Results don’t equate as per the equation.

- Option 4: 8

- Incorrect as it doesn’t satisfy the equation.

- Correct Answer: Option 1: 5