Question : Frank can finish a work in 93 days. Raymond can finish the same work in 98 days while Jack can finish the work in 103 days. How long will it take to finish it if they work together?
Correct Answer 32 17558/28787 days or 32.61 days
Solution & Explanation
Solution
Given,
The number of days required to finish a piece of work by Frank = 93 days
And, the number of days required to finish the same work by Raymond = 98 days
And, the number of days required to finish the same work by Jack = 103 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 93 days the work is done by Frank = 1
∴ The work done by Frank in 1 day = 1/93
Similarly,
∵ In 98 days the work is done by Raymond = 1
∴ The work done by Raymond in 1 day = 1/98
Similarly,
∵ In 103 days the work is done by Jack = 1
∴ The work done by Jack in 1 day = 1/103 part
Now, the work done by Frank, Raymond, and Jack together in 1 day
= Frank's 1 day work + Raymond's 1 day work + Jack's 1 day work
= 1/93 + 1/98 + 1/103
= 10094 + 9579 + 9114/938742
= 28787/938742 part of work
This means in 1 day, 28787/938742 part of work is done by Frank, Raymond and Jack working together.
Now, the number of days required to finish 28787/938742 part of work by Frank, Raymond, and Jack working together = 1
∴ the number of days required to finish the whole work (1 work) by Frank + Raymond + Jack together
= 1/28787/938742
= 1 × 938742/28787 = 938742/28787 days
= 32 17558/28787 days = or 32.61 days
Thus, Frank, Raymond, and Jack working together will finish the total work (1 work) in 32 17558/28787 days = or 32.61 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 Frank = 93 days
And the number of days required to finish the same work by Raymond = 98 days
And the number of days required to finish the work by Jack = 103 days
Thus, the number of days required to finish the work by Frank, Raymond, and Jack together = ?
Here a = 93 days
And, b = 98 days
And, c = 103 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Frank, Raymond, and Jack working together
= 93 × 98 × 103/93 × 98 + 93 × 103 + 98 × 103 days
= 938742/9114 + 9579 + 10094 days
= 938742/28787 days
= 938742/28787 days
= 32 17558/28787 days or 32.61
Thus, Frank, Raymond, and Jack together will finish the work in 32 17558/28787 days or 32.61 days Answer
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