# A and B can finish a work in 6 days and 8 days respectively. They start the work after 2 days C joins them and the work is finished in total 3 days. F

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A and B can finish a work in 6 days and 8 days respectively. They start the work after 2 days C joins them and the work is finished in total 3 days. Find the time C will take to finish the entire work alone?
1. 8
2. 7
3. 6
4. 9

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Correct Answer - Option 1 : 8

Given:

A and B can finish a work in 6 days and 8 days respectively. They start the work after 2 days C joins them and the work is finished in total 3 days.

Formula:

If A and B can together finish it in t days with A and B finishing the work in a and b days respectively,

1/a + 1/b = 1/t

Calculation:

total work will be 24 units.

A’s efficiency = 24/6 = 4

B’s efficiency = 24/8 = 3

Let the efficiency of C be c

ATQ,

7 × 2 + (7 + c) × 1= 24

⇒ 14 + 7 + c = 24

⇒ 21 + c = 24

⇒ c = 24 - 21 = 3

Time taken by C = 24/3 = 8 days