Question

When they work alone, B needs 25% more time to finish a job than A does. They two finish the job in 13 days in the following manner: A works alone till half the job is done, then A and B work together for four days, and finally B works alone to complete the remaining 5% of the job. In how many days can B alone finish the entire job?

• A. 20
• B. 16
• C. 22
• D. 18

Answer 1

The Correct Option is A

We are given that B requires 25% more time than A to finish a job. Let's determine how many days B would take to complete the job working alone. 

Step 1: Let A's time to finish the job = \(x\) days

In one day, A can complete: \[ \frac{1}{x} \ \text{of the job.} \]

Step 2: Time taken by B

Since B needs 25% more time than A: \[ \text{B's time} = 1.25x \ \text{days.} \] Thus, B’s one-day work is: \[ \frac{1}{1.25x} = \frac{0.8}{x} \ \text{of the job.} \]

Step 3: Work distribution

1. First stage: A works alone to complete half the job: \[ \frac{1}{2} \]
2. Second stage: A and B work together for 4 days. Daily work together: \[ \frac{1}{x} + \frac{0.8}{x} = \frac{1.8}{x} \] In 4 days, they complete: \[ \frac{4 \times 1.8}{x} = \frac{7.2}{x} \]
3. Final stage: B works alone to complete the remaining 5%: \[ \frac{1}{20} = 0.05 \]

Step 4: Form the equation

Total work done: \[ \frac{1}{2} + \frac{7.2}{x} + 0.05 = 1 \] Simplify: \[ 0.5 + \frac{7.2}{x} + 0.05 = 1 \] \[ \frac{7.2}{x} = 0.45 \]

Step 5: Solve for \(x\)

\[ x = \frac{7.2}{0.45} = 16 \] So, A can complete the job in **16 days**.

Step 6: Time for B

\[ \text{B's time} = 1.25 \times 16 = 20 \ \text{days} \]

✅ Therefore, B alone can finish the entire job in 20 days.