Question

A and B together can do a piece of work in 12 days. A alone can do it in 20 days. In how many days can B alone do the work?

• A. 24 days
• B. 30 days
• C. 32 days
• D. 36 days

Hint:

Using the LCM method for total work is faster: LCM of 12 and 20 is 60 units. Combined efficiency is 5 units/day, A's efficiency is 3 units/day. Thus, B's efficiency is 2 units/day. Time taken by B = 60/2 = 30 days.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
This time and work problem provides the completion time for a joint effort and for one individual, requiring us to calculate the solo completion time for the second individual.
Step 2: Key Formula or Approach:
An individual finishing a job in \(x\) days has a daily work rate of \(\frac{1}{x}\).
The joint work rate is the sum of individual rates: \(\text{Rate}(A+B) = \text{Rate}(A) + \text{Rate}(B)\).
Step 3: Detailed Explanation:
Since A and B together finish the job in 12 days, their combined daily work rate is:
\[ \text{Rate}(A+B) = \frac{1}{12} \] A working alone takes 20 days, meaning A's daily work rate is:
\[ \text{Rate}(A) = \frac{1}{20} \] Let B's daily work rate be \(\frac{1}{x}\), with \(x\) representing B's solo completion time.
\[ \text{Rate}(B) = \text{Rate}(A+B) - \text{Rate}(A) \] \[ \text{Rate}(B) = \frac{1}{12} - \frac{1}{20} \] Finding the least common multiple (LCM) of 12 and 20, which is 60, allows us to subtract the fractions:
\[ \text{Rate}(B) = \frac{5}{60} - \frac{3}{60} = \frac{2}{60} = \frac{1}{30} \] Because B completes \(\frac{1}{30}\) of the work per day, B will take 30 days to finish the job alone.
Step 4: Final Answer:
The correct choice is (B).