M alone can do a work in 50 days. M is 10% less efficient that N. In how many days can N alone do the same work ?

Options

A. 60 days
B. 45 days
C. 40 days
D. 43 days

Answer

To solve the problem step by step, we can follow these steps:

### Step 1: Determine M's Efficiency
M can complete the work in 50 days. Therefore, M's efficiency can be calculated as follows:

\[ \text{Efficiency of M} = \frac{\text{Total Work}}{\text{Days taken by M}} = \frac{W}{50} \]

### Step 2: Relate M's Efficiency to N's Efficiency
It is given that M is 10% less efficient than N. If we assume N's efficiency is 100 units, then M's efficiency will be:

\[ \text{Efficiency of M} = 100 - 10\% \text{ of } 100 = 90 \]

### Step 3: Set Up the Equation for Total Work
Using the efficiency of M, we can express the total work (W) in terms of M's efficiency:

\[ W = \text{Efficiency of M} \times \text{Days taken by M} = 90 \times 50 = 4500 \text{ units of work} \]

### Step 4: Calculate N's Days to Complete the Same Work
Now we can use N's efficiency to find out how many days N would take to complete the same work. Since N's efficiency is 100, we can set up the equation:

\[ W = \text{Efficiency of N} \times \text{Days taken by N} \]

Substituting the values we have:

\[ 4500 = 100 \times \text{Days taken by N} \]

### Step 5: Solve for Days Taken by N
To find the number of days N will take, we can rearrange the equation:

\[ \text{Days taken by N} = \frac{4500}{100} = 45 \]

### Final Answer
N alone can complete the work in **45 days**.

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