A does a work in 20 days and B does the same work in 30 days. In how many days they together will do the same work?

Options

A. a. 10 days
B. b. 16 days
C. c. 12 days
D. d. 14 days

Answer

To solve the problem step by step, we will first determine the work done by A and B individually, then calculate their combined efficiency, and finally find out how many days they will take to complete the work together.

### Step 1: Determine the work done by A and B
- A can complete the work in 20 days.
- B can complete the same work in 30 days.

### Step 2: Calculate the work done per day by A and B
- Work done by A in one day = 1/20 of the work
- Work done by B in one day = 1/30 of the work

### Step 3: Find the Least Common Multiple (LCM) of the days
- The LCM of 20 and 30 is 60. This will help us find a common measure of work.

### Step 4: Calculate the amount of work done by A and B in terms of LCM
- In 60 days:
- A's work = 60 / 20 = 3 (A can do 3 parts of the work)
- B's work = 60 / 30 = 2 (B can do 2 parts of the work)

### Step 5: Calculate total work done by A and B together
- Total work done by A and B together in one day = (1/20 + 1/30)
- To add these fractions, we find a common denominator:
- The common denominator of 20 and 30 is 60.
- A's work in terms of 60 = 3/60
- B's work in terms of 60 = 2/60
- Total work done together in one day = 3/60 + 2/60 = 5/60

### Step 6: Calculate the total time taken to complete the work together
- Total work = 1 (the whole work)
- Total efficiency = 5/60
- Days taken = Total work / Total efficiency = 1 / (5/60) = 60/5 = 12 days

### Conclusion
A and B together will complete the work in **12 days**.

---