Question : Alexander can finish a work in 91 days. Patrick can finish the same work in 96 days while Raymond can finish the work in 101 days. How long will it take to finish it if they work together?
Correct Answer 31 26023/27623 days or 31.942 days
Solution & Explanation
Solution
Given,
The number of days required to finish a piece of work by Alexander = 91 days
And, the number of days required to finish the same work by Patrick = 96 days
And, the number of days required to finish the same work by Raymond = 101 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 91 days the work is done by Alexander = 1
∴ The work done by Alexander in 1 day = 1/91
Similarly,
∵ In 96 days the work is done by Patrick = 1
∴ The work done by Patrick in 1 day = 1/96
Similarly,
∵ In 101 days the work is done by Raymond = 1
∴ The work done by Raymond in 1 day = 1/101 part
Now, the work done by Alexander, Patrick, and Raymond together in 1 day
= Alexander's 1 day work + Patrick's 1 day work + Raymond's 1 day work
= 1/91 + 1/96 + 1/101
= 9696 + 9191 + 8736/882336
= 27623/882336 part of work
This means in 1 day, 27623/882336 part of work is done by Alexander, Patrick and Raymond working together.
Now, the number of days required to finish 27623/882336 part of work by Alexander, Patrick, and Raymond working together = 1
∴ the number of days required to finish the whole work (1 work) by Alexander + Patrick + Raymond together
= 1/27623/882336
= 1 × 882336/27623 = 882336/27623 days
= 31 26023/27623 days = or 31.942 days
Thus, Alexander, Patrick, and Raymond working together will finish the total work (1 work) in 31 26023/27623 days = or 31.942 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 Alexander = 91 days
And the number of days required to finish the same work by Patrick = 96 days
And the number of days required to finish the work by Raymond = 101 days
Thus, the number of days required to finish the work by Alexander, Patrick, and Raymond together = ?
Here a = 91 days
And, b = 96 days
And, c = 101 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Alexander, Patrick, and Raymond working together
= 91 × 96 × 101/91 × 96 + 91 × 101 + 96 × 101 days
= 882336/8736 + 9191 + 9696 days
= 882336/27623 days
= 882336/27623 days
= 31 26023/27623 days or 31.942
Thus, Alexander, Patrick, and Raymond together will finish the work in 31 26023/27623 days or 31.942 days Answer
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