Question:
Daniel can finish a work in 23 days. Matthew can finish the same work in 24 days while Anthony can finish the work in 25 days. How long will it take to finish it if they work together?
Correct Answer
7 1711/1727 days or 7.991 days
Solution And Explanation
Solution
Given,
The number of days required to finish a piece of work by Daniel = 23 days
And, the number of days required to finish the same work by Matthew = 24 days
And, the number of days required to finish the same work by Anthony = 25 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 23 days the work is done by Daniel = 1
∴ The work done by Daniel in 1 day = 1/23
Similarly,
∵ In 24 days the work is done by Matthew = 1
∴ The work done by Matthew in 1 day = 1/24
Similarly,
∵ In 25 days the work is done by Anthony = 1
∴ The work done by Anthony in 1 day = 1/25 part
Now, the work done by Daniel, Matthew, and Anthony together in 1 day
= Daniel's 1 day work + Matthew's 1 day work + Anthony's 1 day work
= 1/23 + 1/24 + 1/25
= 600 + 575 + 552/13800
= 1727/13800 part of work
This means in 1 day, 1727/13800 part of work is done by Daniel, Matthew and Anthony working together.
Now, the number of days required to finish 1727/13800 part of work by Daniel, Matthew, and Anthony working together = 1
∴ the number of days required to finish the whole work (1 work) by Daniel + Matthew + Anthony together
= 1/1727/13800
= 1 × 13800/1727 = 13800/1727 days
= 7 1711/1727 days = or 7.991 days
Thus, Daniel, Matthew, and Anthony working together will finish the total work (1 work) in 7 1711/1727 days = or 7.991 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 = 23 days
And the number of days required to finish the same work by Matthew = 24 days
And the number of days required to finish the work by Anthony = 25 days
Thus, the number of days required to finish the work by Daniel, Matthew, and Anthony together = ?
Here a = 23 days
And, b = 24 days
And, c = 25 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Daniel, Matthew, and Anthony working together
= 23 × 24 × 25/23 × 24 + 23 × 25 + 24 × 25 days
= 13800/552 + 575 + 600 days
= 13800/1727 days
= 13800/1727 days
= 7 1711/1727 days or 7.991
Thus, Daniel, Matthew, and Anthony together will finish the work in 7 1711/1727 days or 7.991 days Answer
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