CAT 2018 Slot 1 — QA Question 12
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?
Answer & solution
- A
18
- B
22
- C
16
20
Ratio of time taken by A and B to complete a certain task = 4 : 5.
∴ Ratio of their efficiencies = 5 : 4.
Now, A completes 50% of the work alone and B completes 5% of the work alone. That means, A and B together complete 45% of the work together in 4 days.
Out of this 45%, work done by A and B individually will be in the ratio of their efficiencies.
∴ Work done by B in 4 days = 4/9th of 45% = 20%. [Since the ratio of their efficiencies is 5 : 4]
⇒ B completes 20% (i.e., 1/5th) of the work in 4 days.
Thus, B alone can finish the entire job in 20 days.
Hence, option (d).