Ram can do a piece of work in 6 days and Shyam can finish the same work in 12 days. How much work will be finished if both work together for 2 days ?

Options

A. One - fourth of the work
B. One - third of the work
C. Half of the work
D. Whole of the work

Answer

To solve the problem step by step, we will determine how much work Ram and Shyam can complete together in 2 days.

### Step 1: Determine Ram's work rate
Ram can complete the work in 6 days. Therefore, the amount of work Ram can do in one day is:
\[ \text{Work done by Ram in 1 day} = \frac{1}{6} \]

### Step 2: Determine Shyam's work rate
Shyam can complete the same work in 12 days. Therefore, the amount of work Shyam can do in one day is:
\[ \text{Work done by Shyam in 1 day} = \frac{1}{12} \]

### Step 3: Calculate the combined work rate
When Ram and Shyam work together, their combined work done in one day is the sum of their individual work rates:
\[ \text{Combined work in 1 day} = \frac{1}{6} + \frac{1}{12} \]

### Step 4: Find a common denominator
To add the fractions, we need a common denominator. The least common multiple (LCM) of 6 and 12 is 12. We can rewrite \(\frac{1}{6}\) as \(\frac{2}{12}\):
\[ \text{Combined work in 1 day} = \frac{2}{12} + \frac{1}{12} = \frac{3}{12} \]

### Step 5: Simplify the combined work rate
Now, simplify \(\frac{3}{12}\):
\[ \frac{3}{12} = \frac{1}{4} \]
So, together, Ram and Shyam can complete \(\frac{1}{4}\) of the work in one day.

### Step 6: Calculate the work done in 2 days
To find out how much work they can finish in 2 days, we multiply their combined work rate by 2:
\[ \text{Work done in 2 days} = 2 \times \frac{1}{4} = \frac{2}{4} = \frac{1}{2} \]

### Conclusion
Thus, if Ram and Shyam work together for 2 days, they will complete \(\frac{1}{2}\) of the work.

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