Question:
John can finish a work in 9 days. David can finish the same work in 14 days while William can finish the work in 19 days. How long will it take to finish it if they work together?
Correct Answer
4 142/563 days or 4.252 days
Solution And Explanation
Solution
Given,
The number of days required to finish a piece of work by John = 9 days
And, the number of days required to finish the same work by David = 14 days
And, the number of days required to finish the same work by William = 19 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 9 days the work is done by John = 1
∴ The work done by John in 1 day = 1/9
Similarly,
∵ In 14 days the work is done by David = 1
∴ The work done by David in 1 day = 1/14
Similarly,
∵ In 19 days the work is done by William = 1
∴ The work done by William in 1 day = 1/19 part
Now, the work done by John, David, and William together in 1 day
= John's 1 day work + David's 1 day work + William's 1 day work
= 1/9 + 1/14 + 1/19
= 266 + 171 + 126/2394
= 563/2394 part of work
This means in 1 day, 563/2394 part of work is done by John, David and William working together.
Now, the number of days required to finish 563/2394 part of work by John, David, and William working together = 1
∴ the number of days required to finish the whole work (1 work) by John + David + William together
= 1/563/2394
= 1 × 2394/563 = 2394/563 days
= 4 142/563 days = or 4.252 days
Thus, John, David, and William working together will finish the total work (1 work) in 4 142/563 days = or 4.252 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 = 9 days
And the number of days required to finish the same work by David = 14 days
And the number of days required to finish the work by William = 19 days
Thus, the number of days required to finish the work by John, David, and William together = ?
Here a = 9 days
And, b = 14 days
And, c = 19 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when John, David, and William working together
= 9 × 14 × 19/9 × 14 + 9 × 19 + 14 × 19 days
= 2394/126 + 171 + 266 days
= 2394/563 days
= 2394/563 days
= 4 142/563 days or 4.252
Thus, John, David, and William together will finish the work in 4 142/563 days or 4.252 days Answer
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