Manju takes 16 days to complete a work. If she works with her friend Jenny they complete it in 12 days. How many days will it take for Jenny to complete the work alone?
A. 48
B. 32
C. 36
D. 24

Options

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

Answer

To solve the problem, we need to determine how many days it will take for Jenny to complete the work alone, given that Manju takes 16 days to complete the work and together they complete it in 12 days.

### Step-by-Step Solution:

1. **Determine the Total Work**:
- Let's assume the total work is represented in terms of work units. We can use the Least Common Multiple (LCM) of the days taken by Manju and the days taken by both together.
- The LCM of 16 days (Manju) and 12 days (together) is 48. Thus, we can consider the total work to be 48 work units.

2. **Calculate Manju's Work Rate**:
- Manju completes the work in 16 days. Therefore, her work rate (work done per day) is:
\[ \text{Manju's work rate} = \frac{48 \text{ work units}}{16 \text{ days}} = 3 \text{ work units per day} \]

3. **Calculate the Combined Work Rate**:
- Together, Manju and Jenny complete the work in 12 days. Thus, their combined work rate is:
\[ \text{Combined work rate} = \frac{48 \text{ work units}}{12 \text{ days}} = 4 \text{ work units per day} \]

4. **Determine Jenny's Work Rate**:
- We know the combined work rate of Manju and Jenny is 4 work units per day, and Manju's work rate is 3 work units per day. Therefore, Jenny's work rate can be calculated as:
\[ \text{Jenny's work rate} = \text{Combined work rate} - \text{Manju's work rate} = 4 - 3 = 1 \text{ work unit per day} \]

5. **Calculate the Time Taken by Jenny Alone**:
- Now that we know Jenny's work rate, we can find out how many days it will take her to complete the entire work alone. The time taken by Jenny can be calculated as:
\[ \text{Time taken by Jenny} = \frac{\text{Total work}}{\text{Jenny's work rate}} = \frac{48 \text{ work units}}{1 \text{ work unit per day}} = 48 \text{ days} \]

### Conclusion:
Thus, it will take Jenny **48 days** to complete the work alone.