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A, B and C can complete a work in 20, 24 and 30 days respectively. All three of them starts together but after 4 days A leaves the job and B left the job 6 days before the work was completed. C completed the remaining work alone. In how many days was the total work completed?

A, B and C can complete a work in 20, 24 and 30 days respectively. All three of them starts together but after 4 days A leaves the job and B left the job 6 days before the work was completed. C completed the remaining work alone. In how many days was the total work completed? Correct Answer 14

Given:

Time is taken by A to complete a work = 20 days 

Time is taken by B to complete a work = 24 days 

Time is taken by C to complete a work = 30 days 

Formula Used:

Total work = Efficiency × Total time taken

Calculation:

 The  LCM for 20, 24, 30 is (120)

Total work = 120 units

The efficiency of A = 120/20 ⇒ 6 units/day

The efficiency of B = 120/24 ⇒ 5 units/day

The efficiency of C = 120/30 ⇒ 4 units/day

The efficiency of A + B + C = 6 + 5 + 4 ⇒ 15 units/day

The efficiency of B + C = 5 + 4 ⇒ 9 units/day

A, B, C work together for first 4 days = 15 × 4 = 60 units

Remaining work = 120 - 60 ⇒ 60 units

B left the work 6 days before completion

so,C completed the remaining work in last 6 days = 4 × 6 = 24 unit

Middle work = Total work - First work - last work

The B and C complete the work in middle days = 120 - 60 - 24 = 36 units

Time taken by B and C to do the middle days work = 36/9 ⇒ 4 days

Total Time taken to complete the work = 4 + 4 + 6 ⇒ 14 days

∴ In 14 days  the total work completed was completed

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