Question

A alone complete a piece of work in 10/3 days, B and C together can complete the same work in 20/9 days. If B is 25% more efficient than C. Then in how many days A, B, and C together complete the same work?

1. 5/9 days
2. 10/7 days
3. 4/3 days
4. 3/4 days
5. 9/7 days

Answer 1

Correct Answer - Option 3 : 4/3 days

Given:

Time to complete work by A = 10/3 days

Time to complete work by B and C together = 20/9 days

Efficiency of B = 125% efficient than C

Concept used:

One day work = 1/Total days to complete work

Total number of days to complete work = Work/One day work

Calculation:

Time to complete work by A = 10/3 days

One day work of A = 1/(10/3)

⇒ One day work of A = 3/10

Time to complete work by B and C together = 20/9 days

⇒ One day work of B and C together = 1/(20/9)

⇒ One day work of B and C together = 9/20

One day work to complete A, B, and C together = One day work of A + One day work of B and C together

⇒ Required one day work = 3/10 + 9/20

⇒ Required one day work = (6 + 9)/20

⇒ Required one day work = 15/20

⇒ Required one day work = 3/4

Total number of days to complete work = Work/One day work

⇒ Required total days = 1/(3/4)

⇒ Required total days = 4/3 days

∴ 4/3 day to complete same work by A, B, and C.