S and T can finish a work in 50 days. They worked together for 20 days and then left . How much of the work is left

Options

A. 3/5
B. 1/3
C. 1/2
D. 2/5

Answer

To solve the problem, we need to determine how much work S and T have completed together in 20 days and how much work is left after that.

### Step-by-step Solution:

1. **Determine the Total Work**:
Since S and T can finish the work together in 50 days, we can assume that the total work is equivalent to 1 unit of work per day. Therefore, the total work can be represented as:
\[ \text{Total Work} = 50 \text{ units} \]

2. **Calculate Work Done in 20 Days**:
If S and T can complete the entire work in 50 days, then in 1 day, they complete:
\[ \text{Work done in 1 day} = \frac{1 \text{ unit}}{50 \text{ days}} = \frac{1}{50} \text{ units} \]
In 20 days, the work done by S and T together will be:
\[ \text{Work done in 20 days} = 20 \times \frac{1}{50} = \frac{20}{50} = \frac{2}{5} \text{ units} \]

3. **Calculate the Remaining Work**:
To find out how much work is left after they have worked for 20 days, we subtract the work done from the total work:
\[ \text{Remaining Work} = \text{Total Work} - \text{Work Done} \]
\[ \text{Remaining Work} = 50 - \frac{2}{5} \text{ units} \]
To perform this subtraction, we need to convert 50 into a fraction with a denominator of 5:
\[ 50 = \frac{250}{5} \]
Now we can subtract:
\[ \text{Remaining Work} = \frac{250}{5} - \frac{2}{5} = \frac{250 - 2}{5} = \frac{248}{5} \text{ units} \]

4. **Final Answer**:
The amount of work left after S and T have worked together for 20 days is:
\[ \text{Remaining Work} = \frac{248}{5} \text{ units} \approx 49.6 \text{ units} \]