Question:
Samuel can finish a work in 87 days. Alexander can finish the same work in 92 days while Frank can finish the work in 97 days. How long will it take to finish it if they work together?
Correct Answer
30 15378/25367 days or 30.606 days
Solution And Explanation
Solution
Given,
The number of days required to finish a piece of work by Samuel = 87 days
And, the number of days required to finish the same work by Alexander = 92 days
And, the number of days required to finish the same work by Frank = 97 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 87 days the work is done by Samuel = 1
∴ The work done by Samuel in 1 day = 1/87
Similarly,
∵ In 92 days the work is done by Alexander = 1
∴ The work done by Alexander in 1 day = 1/92
Similarly,
∵ In 97 days the work is done by Frank = 1
∴ The work done by Frank in 1 day = 1/97 part
Now, the work done by Samuel, Alexander, and Frank together in 1 day
= Samuel's 1 day work + Alexander's 1 day work + Frank's 1 day work
= 1/87 + 1/92 + 1/97
= 8924 + 8439 + 8004/776388
= 25367/776388 part of work
This means in 1 day, 25367/776388 part of work is done by Samuel, Alexander and Frank working together.
Now, the number of days required to finish 25367/776388 part of work by Samuel, Alexander, and Frank working together = 1
∴ the number of days required to finish the whole work (1 work) by Samuel + Alexander + Frank together
= 1/25367/776388
= 1 × 776388/25367 = 776388/25367 days
= 30 15378/25367 days = or 30.606 days
Thus, Samuel, Alexander, and Frank working together will finish the total work (1 work) in 30 15378/25367 days = or 30.606 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 Samuel = 87 days
And the number of days required to finish the same work by Alexander = 92 days
And the number of days required to finish the work by Frank = 97 days
Thus, the number of days required to finish the work by Samuel, Alexander, and Frank together = ?
Here a = 87 days
And, b = 92 days
And, c = 97 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Samuel, Alexander, and Frank working together
= 87 × 92 × 97/87 × 92 + 87 × 97 + 92 × 97 days
= 776388/8004 + 8439 + 8924 days
= 776388/25367 days
= 776388/25367 days
= 30 15378/25367 days or 30.606
Thus, Samuel, Alexander, and Frank together will finish the work in 30 15378/25367 days or 30.606 days Answer
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