Question : Anthony can finish a work in 27 days. Mark can finish the same work in 28 days while Donald can finish the work in 29 days. How long will it take to finish it if they work together?
Correct Answer 9 765/2351 days or 9.325 days
Solution & Explanation
Solution
Given,
The number of days required to finish a piece of work by Anthony = 27 days
And, the number of days required to finish the same work by Mark = 28 days
And, the number of days required to finish the same work by Donald = 29 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 Anthony = 1
∴ The work done by Anthony in 1 day = 1/27
Similarly,
∵ In 28 days the work is done by Mark = 1
∴ The work done by Mark in 1 day = 1/28
Similarly,
∵ In 29 days the work is done by Donald = 1
∴ The work done by Donald in 1 day = 1/29 part
Now, the work done by Anthony, Mark, and Donald together in 1 day
= Anthony's 1 day work + Mark's 1 day work + Donald's 1 day work
= 1/27 + 1/28 + 1/29
= 812 + 783 + 756/21924
= 2351/21924 part of work
This means in 1 day, 2351/21924 part of work is done by Anthony, Mark and Donald working together.
Now, the number of days required to finish 2351/21924 part of work by Anthony, Mark, and Donald working together = 1
∴ the number of days required to finish the whole work (1 work) by Anthony + Mark + Donald together
= 1/2351/21924
= 1 × 21924/2351 = 21924/2351 days
= 9 765/2351 days = or 9.325 days
Thus, Anthony, Mark, and Donald working together will finish the total work (1 work) in 9 765/2351 days = or 9.325 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 Anthony = 27 days
And the number of days required to finish the same work by Mark = 28 days
And the number of days required to finish the work by Donald = 29 days
Thus, the number of days required to finish the work by Anthony, Mark, and Donald together = ?
Here a = 27 days
And, b = 28 days
And, c = 29 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Anthony, Mark, and Donald working together
= 27 × 28 × 29/27 × 28 + 27 × 29 + 28 × 29 days
= 21924/756 + 783 + 812 days
= 21924/2351 days
= 21924/2351 days
= 9 765/2351 days or 9.325
Thus, Anthony, Mark, and Donald together will finish the work in 9 765/2351 days or 9.325 days Answer
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