S can finish 50% of a work in a day . T can do 25% of the work in day. Both of them together will finish the work in____days.
A. 1
B. 2
C. 1.33
D. 3

Options

A. A
B. C
C. D
D. B

Answer

To solve the problem, we need to determine how many days S and T will take to finish the work together based on their individual work rates.

### Step-by-Step Solution:

1. **Determine Individual Work Rates:**
- S can finish 50% of the work in 1 day. Therefore, in terms of the whole work:
\[ \text{Work done by S in 1 day} = 0.5 \text{ (or } \frac{1}{2} \text{ of the work)} \]
This means S can complete the entire work in:
\[ \text{Total days for S} = \frac{1}{0.5} = 2 \text{ days} \]

- T can finish 25% of the work in 1 day. Therefore, in terms of the whole work:
\[ \text{Work done by T in 1 day} = 0.25 \text{ (or } \frac{1}{4} \text{ of the work)} \]
This means T can complete the entire work in:
\[ \text{Total days for T} = \frac{1}{0.25} = 4 \text{ days} \]

2. **Calculate Individual Efficiencies:**
- The efficiency of S (work done per day) is:
\[ \text{Efficiency of S} = \frac{1}{2} \text{ (work/day)} \]
- The efficiency of T (work done per day) is:
\[ \text{Efficiency of T} = \frac{1}{4} \text{ (work/day)} \]

3. **Combine Efficiencies:**
- The combined efficiency of S and T when working together is:
\[ \text{Combined Efficiency} = \text{Efficiency of S} + \text{Efficiency of T} = \frac{1}{2} + \frac{1}{4} \]
- To add these fractions, find a common denominator (which is 4):
\[ \frac{1}{2} = \frac{2}{4} \]
Thus,
\[ \text{Combined Efficiency} = \frac{2}{4} + \frac{1}{4} = \frac{3}{4} \text{ (work/day)} \]

4. **Calculate Total Days to Complete the Work:**
- The total work is considered as 1 (whole work).
- The total days required to complete the work together is given by:
\[ \text{Total Days} = \frac{\text{Total Work}}{\text{Combined Efficiency}} = \frac{1}{\frac{3}{4}} = \frac{4}{3} \text{ days} \]
- Converting \(\frac{4}{3}\) days to a decimal gives approximately:
\[ 1.33 \text{ days} \]

### Final Answer:
Both S and T together will finish the work in approximately **1.33 days**.