A and B Can finish a work together in 30 days. B and C can finish the same work together in 24 days and A and C can finish the work together in 40 days. If all three Work together. how long Will it take them to complete the Work?

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  1. 15 days
  2. 10 days
  3. 20 days
  4. 5 days

Answer (Detailed Solution Below)

Option 3 : 20 days
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Given:

A and B together can finish the work in 30 days.

B and C together can finish the work in 24 days.

A and C together can finish the work in 40 days.

Calculation:

Let the amount of work be 1 unit.

If A and B can finish the work in 30 days, then A + B's work rate is 1/30 units per day.

If B and C can finish the work in 24 days, then B + C's work rate is 1/24 units per day.

If A and C can finish the work in 40 days, then A + C's work rate is 1/40 units per day.

We have the following equations based on the work rates:

A + B = 1/30

B + C = 1/24

A + C = 1/40

Adding all three equations:

(A + B) + (B + C) + (A + C) = 1/30 + 1/24 + 1/40

2A + 2B + 2C = 1/30 + 1/24 + 1/40

Divide both sides by 2:

A + B + C = 1/60 + 1/48 + 1/80

A + B + C = 4/240 + 5/240 + 3/240 = 12/240 = 1/20

This means that A, B, and C together can complete 1/20 of the work per day.

Therefore, the time taken to complete the work together is:

Time = 1 / (1/20) = 20 days

∴ The time taken by A, B, and C to complete the work together is 20 days.

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