Question:
Paul can finish a work in 35 days. Andrew can finish the same work in 36 days while Joshua can finish the work in 37 days. How long will it take to finish it if they work together?
Correct Answer
11 3863/3887 days or 11.994 days
Solution And Explanation
Solution
Given,
The number of days required to finish a piece of work by Paul = 35 days
And, the number of days required to finish the same work by Andrew = 36 days
And, the number of days required to finish the same work by Joshua = 37 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 35 days the work is done by Paul = 1
∴ The work done by Paul in 1 day = 1/35
Similarly,
∵ In 36 days the work is done by Andrew = 1
∴ The work done by Andrew in 1 day = 1/36
Similarly,
∵ In 37 days the work is done by Joshua = 1
∴ The work done by Joshua in 1 day = 1/37 part
Now, the work done by Paul, Andrew, and Joshua together in 1 day
= Paul's 1 day work + Andrew's 1 day work + Joshua's 1 day work
= 1/35 + 1/36 + 1/37
= 1332 + 1295 + 1260/46620
= 3887/46620 part of work
This means in 1 day, 3887/46620 part of work is done by Paul, Andrew and Joshua working together.
Now, the number of days required to finish 3887/46620 part of work by Paul, Andrew, and Joshua working together = 1
∴ the number of days required to finish the whole work (1 work) by Paul + Andrew + Joshua together
= 1/3887/46620
= 1 × 46620/3887 = 46620/3887 days
= 11 3863/3887 days = or 11.994 days
Thus, Paul, Andrew, and Joshua working together will finish the total work (1 work) in 11 3863/3887 days = or 11.994 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 Paul = 35 days
And the number of days required to finish the same work by Andrew = 36 days
And the number of days required to finish the work by Joshua = 37 days
Thus, the number of days required to finish the work by Paul, Andrew, and Joshua together = ?
Here a = 35 days
And, b = 36 days
And, c = 37 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Paul, Andrew, and Joshua working together
= 35 × 36 × 37/35 × 36 + 35 × 37 + 36 × 37 days
= 46620/1260 + 1295 + 1332 days
= 46620/3887 days
= 46620/3887 days
= 11 3863/3887 days or 11.994
Thus, Paul, Andrew, and Joshua together will finish the work in 11 3863/3887 days or 11.994 days Answer
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