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A is thrice as productive as C. Together they can complete a job in 22.5 days. If B joins them after they have worked for 15 days, then in how many days can they finish the rest of the job, while B alone can do the job in 15 days?

A is thrice as productive as C. Together they can complete a job in 22.5 days. If B joins them after they have worked for 15 days, then in how many days can they finish the rest of the job, while B alone can do the job in 15 days? Correct Answer 3

Shortcut Trick

Work = Efficiency × Time

According to the question 

Efficiency of A = 3

Efficiency of C = 1 

Let the total work be 4 × 22.5 = 90

So, the Efficiency of B = 90 ÷ 15 = 6 unit per day

Accroding to the question 

15 days work of (A + C) = 15 × 4 = 60

Rest work = (90 - 60) units = 30 units 

Now, Combined efficiency of A + B + C = 10 

Time to complete the remaining work = 30 ÷ 10 = 3 days 

∴ The required time is 3 days.

 

Remaining job is (1 - 2/3) = 1/3 part

B alone can do the job in 15 days

⇒ In 1 day B can do 1/15 part of the job

Together in 1 day A, B and C can do (1/22.5 + 1/15) part of the job

⇒ (2 + 3)/45

⇒ 5/45

⇒ 1/9 part of the job

⇒ Together A, B and C can complete the job in 9 days

To complete the remaining 1/3 part of the job they together will take time (9/3) = 3 days.

∴ in 3 days they will complete the rest of the job.

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