Question

When A and B work together then they take 4 hours to complete a piece of work. When B alone works at 75% of his efficiency then he takes 8 hours to complete half of the piece of work. Find the number of hours A alone will take to complete the piece of work if he works at 75% his efficiency?

Answer 1

Step-by-step explanation:

Solution

Given:

• A and B working together will complete a job in 7.5 days

• A works alone for few days and completes half the job

• After that, B takes over and completes the remaining half of the job, working alone

• Total time taken to complete the job = 20 days

• A is more efficient than B

To find:

• The time taken by B alone to complete the entire job

Approach and Working:

• A + B one day’s work =

Let us assume that A works for x days to complete half the job

• Implies, A’s one day work =

This implies, B takes 20 – x days to complete the remaining half of the work

• Implies, B’s one day work =

Thus,

• Implies,

Simplifying this, we get,

• x * (20 – x) = 5 * 15

Comparing the terms on both sides, we can infer that x = 5

• Thus, B’s one day work =

Therefore, B alone takes 30 days to complete the entire job

Hence, the correct answer is Option C

Answer: C