Question

A can do a piece of work in 9 days, B can do it in 12 days and C can do it in 30 days. The efficiency of D is given to be twice the efficiency of C. If A worked for 1 day, B worked for 2 days and C worked for 3 days. Find the number of days D will take to complete the remaining work alone?

1. 20/3 days
2. 25/3 days
3. 23/3 days
4. 28/3 days
5. None of the above

Answer 1

Correct Answer - Option 4 : 28/3 days

Given:

A can do a piece of work in = 9 days

B can do a piece of work in = 12 days

C can do a piece of work in = 30 days

The efficiency of D = 2 × Efficiency of C

A worked for = 1 day

B worked for = 2 days

C worked for = 3 days

Calculation:

Work is done by A in one day = 1/9

Work is done by B in one day = 1/12

Work is done by C in one day = 1/30

The efficiency of D is twice the efficiency of C, work done by D in one day

⇒ 1/15

∴ Remaining work done = 1 – (1/9) – (2/12) – (3/30)

⇒ 1 – [(1/9) + (1/6) + (1/10)]

⇒ 1 – [(10 + 15 + 9)/90]

⇒ 1 – [34/90]

⇒ 56/90

⇒ 28/45

Let the time taken by D to complete the remaining work alone be x.

⇒ x/15 = 28/45

⇒ x = 28/3 days

∴ D alone will take 28/3 days to finish the work.