Question : Matthew can finish a work in 25 days. Anthony can finish the same work in 26 days while Mark can finish the work in 27 days. How long will it take to finish it if they work together?
Correct Answer 8 1334/2027 days or 8.658 days
Solution & Explanation
Solution
Given,
The number of days required to finish a piece of work by Matthew = 25 days
And, the number of days required to finish the same work by Anthony = 26 days
And, the number of days required to finish the same work by Mark = 27 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 25 days the work is done by Matthew = 1
∴ The work done by Matthew in 1 day = 1/25
Similarly,
∵ In 26 days the work is done by Anthony = 1
∴ The work done by Anthony in 1 day = 1/26
Similarly,
∵ In 27 days the work is done by Mark = 1
∴ The work done by Mark in 1 day = 1/27 part
Now, the work done by Matthew, Anthony, and Mark together in 1 day
= Matthew's 1 day work + Anthony's 1 day work + Mark's 1 day work
= 1/25 + 1/26 + 1/27
= 702 + 675 + 650/17550
= 2027/17550 part of work
This means in 1 day, 2027/17550 part of work is done by Matthew, Anthony and Mark working together.
Now, the number of days required to finish 2027/17550 part of work by Matthew, Anthony, and Mark working together = 1
∴ the number of days required to finish the whole work (1 work) by Matthew + Anthony + Mark together
= 1/2027/17550
= 1 × 17550/2027 = 17550/2027 days
= 8 1334/2027 days = or 8.658 days
Thus, Matthew, Anthony, and Mark working together will finish the total work (1 work) in 8 1334/2027 days = or 8.658 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 Matthew = 25 days
And the number of days required to finish the same work by Anthony = 26 days
And the number of days required to finish the work by Mark = 27 days
Thus, the number of days required to finish the work by Matthew, Anthony, and Mark together = ?
Here a = 25 days
And, b = 26 days
And, c = 27 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Matthew, Anthony, and Mark working together
= 25 × 26 × 27/25 × 26 + 25 × 27 + 26 × 27 days
= 17550/650 + 675 + 702 days
= 17550/2027 days
= 17550/2027 days
= 8 1334/2027 days or 8.658
Thus, Matthew, Anthony, and Mark together will finish the work in 8 1334/2027 days or 8.658 days Answer
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