If the work done by (x – 1) men in (x + 1) days and the work done by (x + 2) men in (x – 1) days is in the ratio of 9 : 10, then x is equal to .

Options

A. 5
B. 6
C. 7
D. 8

Answer

To solve the problem, we need to set up the equation based on the information given in the question.

### Step-by-Step Solution:

1. **Identify the Work Done**:
- The work done by (x - 1) men in (x + 1) days is given by:
\[ W_1 = (x - 1)(x + 1) \]
- The work done by (x + 2) men in (x - 1) days is given by:
\[ W_2 = (x + 2)(x - 1) \]

2. **Set Up the Ratio**:
- According to the problem, the ratio of the work done is:
\[ \frac{W_1}{W_2} = \frac{9}{10} \]
- Substituting the expressions for \(W_1\) and \(W_2\):
\[ \frac{(x - 1)(x + 1)}{(x + 2)(x - 1)} = \frac{9}{10} \]

3. **Simplify the Equation**:
- We can cancel out \((x - 1)\) from both sides (assuming \(x \neq 1\)):
\[ \frac{x + 1}{x + 2} = \frac{9}{10} \]

4. **Cross Multiply**:
- Cross multiplying gives us:
\[ 10(x + 1) = 9(x + 2) \]

5. **Expand Both Sides**:
- Expanding both sides:
\[ 10x + 10 = 9x + 18 \]

6. **Rearrange the Equation**:
- Move all terms involving \(x\) to one side and constant terms to the other:
\[ 10x - 9x = 18 - 10 \]
\[ x = 8 \]

### Final Answer:
Thus, the value of \(x\) is:
\[ \boxed{8} \]