M is the thrice as good as work-man as N and together they finish a piece of work in 30 days.In how many days will M alone finish the work?

Options

A. 50
B. 40
C. 60
D. 45

Answer

To solve the problem, we need to determine how many days M alone will take to finish the work, given that M is thrice as efficient as N and together they complete the work in 30 days.

### Step-by-Step Solution:

1. **Understanding the Work Efficiency**:
- Let the work done by N in one day be represented as 1 unit of work.
- Since M is thrice as good as N, the work done by M in one day will be 3 units of work.

2. **Combined Work Rate**:
- Together, M and N can complete the work in 30 days.
- Therefore, the total work done by both in one day is:
\[ \text{Work done by M + Work done by N} = 3 + 1 = 4 \text{ units of work per day} \]

3. **Total Work Calculation**:
- If they complete the work in 30 days, the total work can be calculated as:
\[ \text{Total Work} = \text{Work rate} \times \text{Number of days} = 4 \text{ units/day} \times 30 \text{ days} = 120 \text{ units} \]

4. **M's Work Alone**:
- Now, we need to find out how many days M will take to finish the total work alone.
- Since M does 3 units of work per day, the number of days M will take to finish 120 units of work is:
\[ \text{Days taken by M} = \frac{\text{Total Work}}{\text{Work done by M in one day}} = \frac{120 \text{ units}}{3 \text{ units/day}} = 40 \text{ days} \]

### Final Answer:
M alone will finish the work in **40 days**.