Question:
Joseph can finish a work in 15 days. Thomas can finish the same work in 16 days while Charles can finish the work in 17 days. How long will it take to finish it if they work together?
Correct Answer
5 245/767 days or 5.319 days
Solution And Explanation
Solution
Given,
The number of days required to finish a piece of work by Joseph = 15 days
And, the number of days required to finish the same work by Thomas = 16 days
And, the number of days required to finish the same work by Charles = 17 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 15 days the work is done by Joseph = 1
∴ The work done by Joseph in 1 day = 1/15
Similarly,
∵ In 16 days the work is done by Thomas = 1
∴ The work done by Thomas in 1 day = 1/16
Similarly,
∵ In 17 days the work is done by Charles = 1
∴ The work done by Charles in 1 day = 1/17 part
Now, the work done by Joseph, Thomas, and Charles together in 1 day
= Joseph's 1 day work + Thomas's 1 day work + Charles's 1 day work
= 1/15 + 1/16 + 1/17
= 272 + 255 + 240/4080
= 767/4080 part of work
This means in 1 day, 767/4080 part of work is done by Joseph, Thomas and Charles working together.
Now, the number of days required to finish 767/4080 part of work by Joseph, Thomas, and Charles working together = 1
∴ the number of days required to finish the whole work (1 work) by Joseph + Thomas + Charles together
= 1/767/4080
= 1 × 4080/767 = 4080/767 days
= 5 245/767 days = or 5.319 days
Thus, Joseph, Thomas, and Charles working together will finish the total work (1 work) in 5 245/767 days = or 5.319 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 Joseph = 15 days
And the number of days required to finish the same work by Thomas = 16 days
And the number of days required to finish the work by Charles = 17 days
Thus, the number of days required to finish the work by Joseph, Thomas, and Charles together = ?
Here a = 15 days
And, b = 16 days
And, c = 17 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Joseph, Thomas, and Charles working together
= 15 × 16 × 17/15 × 16 + 15 × 17 + 16 × 17 days
= 4080/240 + 255 + 272 days
= 4080/767 days
= 4080/767 days
= 5 245/767 days or 5.319
Thus, Joseph, Thomas, and Charles together will finish the work in 5 245/767 days or 5.319 days Answer
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