Ganesh, Ram and Sohan together can do a work in 16 days. If Ganesh and Ram together can do the same work in 24 days then, how long will take Sohan alone to do the same work ?

Options

A. 42 days
B. 24 days
C. 36 days
D. 48 days

Answer

To solve the problem, we will use the concept of work done in terms of days. Let's denote the work done by Ganesh, Ram, and Sohan as G, R, and S respectively.

### Step 1: Calculate the work done by Ganesh, Ram, and Sohan together.
Ganesh, Ram, and Sohan together can complete the work in 16 days. Therefore, the work done by them in one day is:
\[ \text{Work done by (G + R + S) in 1 day} = \frac{1}{16} \]

### Step 2: Calculate the work done by Ganesh and Ram together.
Ganesh and Ram together can complete the work in 24 days. Therefore, the work done by them in one day is:
\[ \text{Work done by (G + R) in 1 day} = \frac{1}{24} \]

### Step 3: Set up the equation to find the work done by Sohan alone.
From the above two equations, we can express the work done by Sohan alone:
\[ (G + R + S) - (G + R) = S \]
So, we can write:
\[ S = \left(\frac{1}{16}\right) - \left(\frac{1}{24}\right) \]

### Step 4: Find a common denominator and calculate S.
The common denominator for 16 and 24 is 48. We convert both fractions:
\[ \frac{1}{16} = \frac{3}{48} \]
\[ \frac{1}{24} = \frac{2}{48} \]
Now, substituting back:
\[ S = \frac{3}{48} - \frac{2}{48} = \frac{1}{48} \]

### Step 5: Calculate the time taken by Sohan to complete the work alone.
Since Sohan can do \(\frac{1}{48}\) of the work in one day, the time taken by Sohan to complete the work alone is:
\[ \text{Time taken by Sohan} = \frac{1}{\frac{1}{48}} = 48 \text{ days} \]

### Final Answer:
Sohan alone will take **48 days** to complete the work.

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