Question
Download Solution PDFA 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?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
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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