# A and B can complete a work in 10 days and 6 days respectively, while C can complete the same work in 5 days. A starts work and they work alternativel

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A and B can complete a work in 10 days and 6 days respectively, while C can complete the same work in 5 days. A starts work and they work alternatively, then in how many days work will be completed?
1. 8/3 days
2. 16/3 days
3. 20/3 days
4. 29/7 days

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Correct Answer - Option 3 : 20/3 days

Given:

A can complete the work in 10 days

B can complete the same work in 6 days

C can complete the same work in 5 days

Formula Used:

Work = Efficiency × Time

Calculation:

Let total work of A, B, C be a multiple of 10, 6, 5.

⇒ Total work = 60

Efficiency of A = 60/10

⇒ Efficiency of A = 6

Efficiency of B = 60/6

⇒ Efficiency of B = 10

Efficiency of C = 60/5

⇒ Efficiency of C = 12

Working alternatively means First day A works Second day B works and third day C works and this will continue till the completion of the work

⇒ Cycle of A, B, C repeats in every 3 days

In three days they will complete = 6 + 10 + 12

⇒ 28

In 6 days they will complete = 2 × 28

⇒ 56

Work left after 6 days = 60 – 56

⇒ 4

Now, it is A's turn, time taken by A = 4/6

⇒ 2/3 days

Total time is taken to complete the work = 6 + 2/3

∴ The total time is taken to complete the work is 20/3 days

Alternatively means one person will work on a day and in the sequence.

∴ The work will be completed in 20/3 days.