Mukesh and Dinesh together can complete a work in 120 days. Mukesh alone can complete the work in 150 days. In how many days can Dinesh alone complete the work?

Options

A. 650
B. 720
C. 450
D. 600

Answer

To find out how many days Dinesh alone can complete the work, we can follow these steps:

### Step 1: Determine the work rates of Mukesh and Dinesh
- Mukesh and Dinesh together can complete the work in 120 days. Therefore, their combined work rate is:
\[ \text{Work rate of Mukesh + Dinesh} = \frac{1}{120} \text{ work per day} \]

- Mukesh alone can complete the work in 150 days. Therefore, Mukesh's work rate is:
\[ \text{Work rate of Mukesh} = \frac{1}{150} \text{ work per day} \]

### Step 2: Calculate Dinesh's work rate
- Let Dinesh's work rate be \( \frac{1}{d} \) work per day, where \( d \) is the number of days Dinesh takes to complete the work alone.
- According to the work rates, we can set up the equation:
\[ \frac{1}{150} + \frac{1}{d} = \frac{1}{120} \]

### Step 3: Solve for Dinesh's work rate
- Rearranging the equation gives:
\[ \frac{1}{d} = \frac{1}{120} - \frac{1}{150} \]
- To subtract the fractions, we need a common denominator. The least common multiple (LCM) of 120 and 150 is 600. Thus, we convert the fractions:
\[ \frac{1}{120} = \frac{5}{600}, \quad \frac{1}{150} = \frac{4}{600} \]
- Now substitute back into the equation:
\[ \frac{1}{d} = \frac{5}{600} - \frac{4}{600} = \frac{1}{600} \]

### Step 4: Find Dinesh's days to complete the work
- Taking the reciprocal gives:
\[ d = 600 \]
- Therefore, Dinesh alone can complete the work in 600 days.

### Final Answer:
Dinesh alone can complete the work in **600 days**.

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