Question : Daniel can finish a work in 27 days. Anthony can finish the same work in 32 days while Mark can finish the work in 37 days. How long will it take to finish it if they work together?
Correct Answer 10 1498/3047 days or 10.492 days
Solution & Explanation
Solution
Given,
The number of days required to finish a piece of work by Daniel = 27 days
And, the number of days required to finish the same work by Anthony = 32 days
And, the number of days required to finish the same work by Mark = 37 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 27 days the work is done by Daniel = 1
∴ The work done by Daniel in 1 day = 1/27
Similarly,
∵ In 32 days the work is done by Anthony = 1
∴ The work done by Anthony in 1 day = 1/32
Similarly,
∵ In 37 days the work is done by Mark = 1
∴ The work done by Mark in 1 day = 1/37 part
Now, the work done by Daniel, Anthony, and Mark together in 1 day
= Daniel's 1 day work + Anthony's 1 day work + Mark's 1 day work
= 1/27 + 1/32 + 1/37
= 1184 + 999 + 864/31968
= 3047/31968 part of work
This means in 1 day, 3047/31968 part of work is done by Daniel, Anthony and Mark working together.
Now, the number of days required to finish 3047/31968 part of work by Daniel, Anthony, and Mark working together = 1
∴ the number of days required to finish the whole work (1 work) by Daniel + Anthony + Mark together
= 1/3047/31968
= 1 × 31968/3047 = 31968/3047 days
= 10 1498/3047 days = or 10.492 days
Thus, Daniel, Anthony, and Mark working together will finish the total work (1 work) in 10 1498/3047 days = or 10.492 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 Daniel = 27 days
And the number of days required to finish the same work by Anthony = 32 days
And the number of days required to finish the work by Mark = 37 days
Thus, the number of days required to finish the work by Daniel, Anthony, and Mark together = ?
Here a = 27 days
And, b = 32 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 Daniel, Anthony, and Mark working together
= 27 × 32 × 37/27 × 32 + 27 × 37 + 32 × 37 days
= 31968/864 + 999 + 1184 days
= 31968/3047 days
= 31968/3047 days
= 10 1498/3047 days or 10.492
Thus, Daniel, Anthony, and Mark together will finish the work in 10 1498/3047 days or 10.492 days Answer
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