Question:
Richard can finish a work in 17 days. Thomas can finish the same work in 22 days while Charles can finish the work in 27 days. How long will it take to finish it if they work together?
Correct Answer
7 109/1427 days or 7.076 days
Solution And Explanation
Solution
Given,
The number of days required to finish a piece of work by Richard = 17 days
And, the number of days required to finish the same work by Thomas = 22 days
And, the number of days required to finish the same work by Charles = 27 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 17 days the work is done by Richard = 1
∴ The work done by Richard in 1 day = 1/17
Similarly,
∵ In 22 days the work is done by Thomas = 1
∴ The work done by Thomas in 1 day = 1/22
Similarly,
∵ In 27 days the work is done by Charles = 1
∴ The work done by Charles in 1 day = 1/27 part
Now, the work done by Richard, Thomas, and Charles together in 1 day
= Richard's 1 day work + Thomas's 1 day work + Charles's 1 day work
= 1/17 + 1/22 + 1/27
= 594 + 459 + 374/10098
= 1427/10098 part of work
This means in 1 day, 1427/10098 part of work is done by Richard, Thomas and Charles working together.
Now, the number of days required to finish 1427/10098 part of work by Richard, Thomas, and Charles working together = 1
∴ the number of days required to finish the whole work (1 work) by Richard + Thomas + Charles together
= 1/1427/10098
= 1 × 10098/1427 = 10098/1427 days
= 7 109/1427 days = or 7.076 days
Thus, Richard, Thomas, and Charles working together will finish the total work (1 work) in 7 109/1427 days = or 7.076 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 Richard = 17 days
And the number of days required to finish the same work by Thomas = 22 days
And the number of days required to finish the work by Charles = 27 days
Thus, the number of days required to finish the work by Richard, Thomas, and Charles together = ?
Here a = 17 days
And, b = 22 days
And, c = 27 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Richard, Thomas, and Charles working together
= 17 × 22 × 27/17 × 22 + 17 × 27 + 22 × 27 days
= 10098/374 + 459 + 594 days
= 10098/1427 days
= 10098/1427 days
= 7 109/1427 days or 7.076
Thus, Richard, Thomas, and Charles together will finish the work in 7 109/1427 days or 7.076 days Answer
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