Question : Patrick can finish a work in 95 days. Jack can finish the same work in 100 days while Dennis can finish the work in 105 days. How long will it take to finish it if they work together?
Correct Answer 33 333/1199 days or 33.278 days
Solution & Explanation
Solution
Given,
The number of days required to finish a piece of work by Patrick = 95 days
And, the number of days required to finish the same work by Jack = 100 days
And, the number of days required to finish the same work by Dennis = 105 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 95 days the work is done by Patrick = 1
∴ The work done by Patrick in 1 day = 1/95
Similarly,
∵ In 100 days the work is done by Jack = 1
∴ The work done by Jack in 1 day = 1/100
Similarly,
∵ In 105 days the work is done by Dennis = 1
∴ The work done by Dennis in 1 day = 1/105 part
Now, the work done by Patrick, Jack, and Dennis together in 1 day
= Patrick's 1 day work + Jack's 1 day work + Dennis's 1 day work
= 1/95 + 1/100 + 1/105
= 420 + 399 + 380/39900
= 1199/39900 part of work
This means in 1 day, 1199/39900 part of work is done by Patrick, Jack and Dennis working together.
Now, the number of days required to finish 1199/39900 part of work by Patrick, Jack, and Dennis working together = 1
∴ the number of days required to finish the whole work (1 work) by Patrick + Jack + Dennis together
= 1/1199/39900
= 1 × 39900/1199 = 39900/1199 days
= 33 333/1199 days = or 33.278 days
Thus, Patrick, Jack, and Dennis working together will finish the total work (1 work) in 33 333/1199 days = or 33.278 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 Patrick = 95 days
And the number of days required to finish the same work by Jack = 100 days
And the number of days required to finish the work by Dennis = 105 days
Thus, the number of days required to finish the work by Patrick, Jack, and Dennis together = ?
Here a = 95 days
And, b = 100 days
And, c = 105 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Patrick, Jack, and Dennis working together
= 95 × 100 × 105/95 × 100 + 95 × 105 + 100 × 105 days
= 997500/9500 + 9975 + 10500 days
= 997500/29975 days
= 997500/29975 days
= 997500 ÷ 25/29975 ÷ 25 = 39900/1199 days
= 33 333/1199 days or 33.278
Thus, Patrick, Jack, and Dennis together will finish the work in 33 333/1199 days or 33.278 days Answer
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