If 'A' completes 3/5 of a work in 3 days, 'B' completes 1/5 of the same work in 4 days. If both of them work together, how much time will they take to complete 1/2 of that work?

Question

Accepted Answer

To determine how much time 'A' and 'B' will take to complete 1/2 of the work together, we first need to calculate their individual work rates and then combine them.

### Step 1: Calculate Individual Work Rates

1. **Work Rate of 'A':**
   - 'A' completes 3/5 of the work in 3 days.
   - Therefore, 'A's work rate = (3/5) / 3 = 1/5 of the work per day.

2. **Work Rate of 'B':**
   - 'B' completes 1/5 of the work in 4 days.
   - Therefore, 'B's work rate = (1/5) / 4 = 1/20 of the work per day.

### Step 2: Calculate Combined Work Rate

- When 'A' and 'B' work together, their combined work rate is the sum of their individual work rates.
- Combined work rate = (1/5) + (1/20)
- To add these fractions, find a common denominator, which is 20:
  - (1/5) = 4/20
  - (1/20) = 1/20
- Combined work rate = 4/20 + 1/20 = 5/20 = 1/4 of the work per day.

### Step 3: Calculate Time to Complete 1/2 of the Work

- We need to find out how long it takes to complete 1/2 of the work with a combined work rate of 1/4 of the work per day.
- Let the time taken be 't' days.
- Work done in 't' days = (1/4) * t
- We want this to equal 1/2 of the work:
  - (1/4) * t = 1/2
- Solving for 't':
  - t = (1/2) / (1/4)
  - t = 1/2 * 4/1
  - t = 2 days

### Conclusion

Therefore, 'A' and 'B' working together will take 2 days to complete 1/2 of the work. This supports the given correct answer, which is Option 2.

### Explanation of Incorrect Options

1. **Option 1: $\frac{1}{2} 	ext{days}$**
   - This option suggests that 'A' and 'B' can complete 1/2 of the work in just half a day, which is not possible given their combined work rate of 1/4 of the work per day.

2. **Option 3: $3\frac{1}{2} 	ext{days}$**
   - This option overestimates the time required. Given their combined work rate, they can complete 1/2 of the work in 2 days, not 3.5 days.

3. **Option 4: 4 days**
   - This option also overestimates the time needed. At a rate of 1/4 of the work per day, they would complete the entire work in 4 days, not just 1/2 of it.

Thus, Option 2 is the correct answer, as it accurately reflects the time 'A' and 'B' need to complete 1/2 of the work together.