Question:
James can finish a work in 5 days. John can finish the same work in 10 days while Michael can finish the work in 15 days. How long will it take to finish it if they work together?
Correct Answer
2 8/11 days or 2.727 days
Solution And Explanation
Solution
Given,
The number of days required to finish a piece of work by James = 5 days
And, the number of days required to finish the same work by John = 10 days
And, the number of days required to finish the same work by Michael = 15 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 5 days the work is done by James = 1
∴ The work done by James in 1 day = 1/5
Similarly,
∵ In 10 days the work is done by John = 1
∴ The work done by John in 1 day = 1/10
Similarly,
∵ In 15 days the work is done by Michael = 1
∴ The work done by Michael in 1 day = 1/15 part
Now, the work done by James, John, and Michael together in 1 day
= James's 1 day work + John's 1 day work + Michael's 1 day work
= 1/5 + 1/10 + 1/15
= 6 + 3 + 2/30
= 11/30 part of work
This means in 1 day, 11/30 part of work is done by James, John and Michael working together.
Now, the number of days required to finish 11/30 part of work by James, John, and Michael working together = 1
∴ the number of days required to finish the whole work (1 work) by James + John + Michael together
= 1/11/30
= 1 × 30/11 = 30/11 days
= 2 8/11 days = or 2.727 days
Thus, James, John, and Michael working together will finish the total work (1 work) in 2 8/11 days = or 2.727 days Answer
Shortcut Trick to solve the problems based on time and work using formula
Case: If A can finish a work in a days, 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 required to finish the work
= a × b × c/ab + ac + bc days.
Here given,
The number of days required to finish the work by James = 5 days
And the number of days required to finish the same work by John = 10 days
And the number of days required to finish the work by Michael = 15 days
Thus, the number of days required to finish the work by James, John, and Michael together = ?
Here a = 5 days
And, b = 10 days
And, c = 15 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when James, John, and Michael working together
= 5 × 10 × 15/5 × 10 + 5 × 15 + 10 × 15 days
= 750/50 + 75 + 150 days
= 750/275 days
= 750/275 days
= 750 ÷ 25/275 ÷ 25 = 30/11 days
= 2 8/11 days or 2.727
Thus, James, John, and Michael together will finish the work in 2 8/11 days or 2.727 days Answer
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