A man can do a piece of work in 30 hours. If he works with his son then the same piece of work is finished in 20 hours. If the son works alone he can do the work in

Options

A. 60 hours
B. 50 hours
C. 25 hours
D. 10 hours

Answer

To solve the problem step by step, we can break it down as follows:

### Step 1: Determine the total work done
The man can complete the work in 30 hours. Therefore, if we consider the total work as 60 units (this is the least common multiple of 30 and 20), we can use this to find the efficiencies.

### Step 2: Calculate the efficiency of the man
The efficiency of the man can be calculated as:
\[ \text{Efficiency of Man} = \frac{\text{Total Work}}{\text{Time taken by Man}} = \frac{60}{30} = 2 \text{ units/hour} \]

### Step 3: Calculate the efficiency of the man and son together
When the man works with his son, they can complete the work in 20 hours. Therefore, their combined efficiency is:
\[ \text{Efficiency of Man + Son} = \frac{\text{Total Work}}{\text{Time taken by Man + Son}} = \frac{60}{20} = 3 \text{ units/hour} \]

### Step 4: Calculate the efficiency of the son
To find the efficiency of the son, we subtract the efficiency of the man from the combined efficiency:
\[ \text{Efficiency of Son} = \text{Efficiency of Man + Son} - \text{Efficiency of Man} = 3 - 2 = 1 \text{ unit/hour} \]

### Step 5: Calculate the time taken by the son to complete the work alone
Now that we know the efficiency of the son, we can find out how long it will take him to complete the entire work alone:
\[ \text{Time taken by Son} = \frac{\text{Total Work}}{\text{Efficiency of Son}} = \frac{60}{1} = 60 \text{ hours} \]

### Final Answer
The son can complete the work alone in **60 hours**.

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