Question:
If A can do a piece of work in 2 days, B can do the same piece of work in 3 days, while C alone can do the same work in 4 days. Find the number of days to finish the work when they all will work together.
Correct Answer
12/13 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by A = 2
And, the number of days to finish the work by B = 3
And, the number of days to finish the work by C = 4
Thus, the number of days require to finish the work by working A, B, and C together = ?
Since in 2 days, A alone can finish the work.
∴ In 1 day work done by A = 1/2 part
Similarly,
Since in 3 days, B alone can finish the work.
∴ In 1 day work done by B = 1/3 part
Similarly,
Since in 4 days, C alone can finish the work.
∴ In 1 day work done by C = 1/4 part
Now, work done in 1 day by A, B and C working together
= A's 1 day work + B's 1 day work + C's 1 day work
= 1/2 + 1/3 + 1/4
= 6 + 4 + 3/12
⇒ Work done in 1 day by A, B, and C together = 13/12
Now, ∵ Number of days required to finish 13/12 part work by A, B, and C together = 1
∴ Number of days required to finish 1 work by A, B, and C together = 1/13/12
= 1 × 12/13 days
= 12/13 days
Thus, by working together A, B, C will finish the work in 12/13 days Answer
Shortcut Trick to solve the problems based on time and work using formula
Case (1): If A can finish a work in "a" days, and B can finish the same work in "b" days,
then working together the number of days require to finish the work
= a × b/a + b days.
Case (2): If A can finish a work in "a" days, and B can finish the same work in "b" days, and C can finish the work in "c" days,
then working together the number of days require to finish the work
= a × b × c/ab + bc + ac days.
Here given,
The number of days to finish the work by A = 2 days
And, the number of days to finish the same work by B = 3 days
And, the number of days to finish the same work by C = 4 days
Thus, the number of days to finish the work by A, B, and C together = ?
Here "a" = 2 days
And, "b" = 3 days
And, "c" = 4 days
Thus, using formula a × b × c/ab + bc + ac days
The number of days require to finish the work when A, B, and C together
= 2 × 3 × 4/(2 ×3) + (3 × 4) + (2 × 4) days
= 24/6 + 12 + 8 days
= 24/26 days
= 24 12/26 13 days
= 12/13 days
Thus, by working together A, B, C will finish the work in 12/13 days Answer
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