A and B can together complete a tsk in 21 days. If a alone takes 42 days to complete the task, the number of days that B would take to do the task alone is :

Options

A. 42
B. 36
C. 27
D. 32

Answer

To solve the problem step by step, we can follow these calculations:

### Step 1: Understand the given information
- A and B together can complete the task in 21 days.
- A alone can complete the task in 42 days.

### Step 2: Calculate the total work
To find the total work, we can use the least common multiple (LCM) of the days taken by A and the days taken by A and B together.

- LCM of 21 and 42 is 42.
(Since 42 is the maximum time taken by A, it is also the LCM.)

### Step 3: Calculate the efficiencies
- Efficiency of A = Total Work / Time taken by A = 42 / 42 = 1 (work units per day)
- Efficiency of A and B together = Total Work / Time taken by A and B together = 42 / 21 = 2 (work units per day)

### Step 4: Find the efficiency of B
- Efficiency of B = Efficiency of A and B together - Efficiency of A
- Efficiency of B = 2 - 1 = 1 (work units per day)

### Step 5: Calculate the time taken by B to complete the task alone
Using the formula:
- Work = Time × Efficiency
We can rearrange this to find the time taken by B:
- Time of B = Total Work / Efficiency of B
- Time of B = 42 / 1 = 42 days

### Final Answer
B would take 42 days to complete the task alone.

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