Question:
John can finish a work in 5 days. Michael can finish the same work in 6 days while David can finish the work in 7 days. How long will it take to finish it if they work together?
Correct Answer
1 103/107 days or 1.963 days
Solution And Explanation
Solution
Given,
The number of days required to finish a piece of work by John = 5 days
And, the number of days required to finish the same work by Michael = 6 days
And, the number of days required to finish the same work by David = 7 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 John = 1
∴ The work done by John in 1 day = 1/5
Similarly,
∵ In 6 days the work is done by Michael = 1
∴ The work done by Michael in 1 day = 1/6
Similarly,
∵ In 7 days the work is done by David = 1
∴ The work done by David in 1 day = 1/7 part
Now, the work done by John, Michael, and David together in 1 day
= John's 1 day work + Michael's 1 day work + David's 1 day work
= 1/5 + 1/6 + 1/7
= 42 + 35 + 30/210
= 107/210 part of work
This means in 1 day, 107/210 part of work is done by John, Michael and David working together.
Now, the number of days required to finish 107/210 part of work by John, Michael, and David working together = 1
∴ the number of days required to finish the whole work (1 work) by John + Michael + David together
= 1/107/210
= 1 × 210/107 = 210/107 days
= 1 103/107 days = or 1.963 days
Thus, John, Michael, and David working together will finish the total work (1 work) in 1 103/107 days = or 1.963 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 John = 5 days
And the number of days required to finish the same work by Michael = 6 days
And the number of days required to finish the work by David = 7 days
Thus, the number of days required to finish the work by John, Michael, and David together = ?
Here a = 5 days
And, b = 6 days
And, c = 7 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when John, Michael, and David working together
= 5 × 6 × 7/5 × 6 + 5 × 7 + 6 × 7 days
= 210/30 + 35 + 42 days
= 210/107 days
= 210/107 days
= 1 103/107 days or 1.963
Thus, John, Michael, and David together will finish the work in 1 103/107 days or 1.963 days Answer
Similar Questions
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