Question : Christopher can finish a work in 21 days. Daniel can finish the same work in 22 days while Matthew can finish the work in 23 days. How long will it take to finish it if they work together?
Correct Answer 7 469/1451 days or 7.323 days
Solution & Explanation
Solution
Given,
The number of days required to finish a piece of work by Christopher = 21 days
And, the number of days required to finish the same work by Daniel = 22 days
And, the number of days required to finish the same work by Matthew = 23 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 21 days the work is done by Christopher = 1
∴ The work done by Christopher in 1 day = 1/21
Similarly,
∵ In 22 days the work is done by Daniel = 1
∴ The work done by Daniel in 1 day = 1/22
Similarly,
∵ In 23 days the work is done by Matthew = 1
∴ The work done by Matthew in 1 day = 1/23 part
Now, the work done by Christopher, Daniel, and Matthew together in 1 day
= Christopher's 1 day work + Daniel's 1 day work + Matthew's 1 day work
= 1/21 + 1/22 + 1/23
= 506 + 483 + 462/10626
= 1451/10626 part of work
This means in 1 day, 1451/10626 part of work is done by Christopher, Daniel and Matthew working together.
Now, the number of days required to finish 1451/10626 part of work by Christopher, Daniel, and Matthew working together = 1
∴ the number of days required to finish the whole work (1 work) by Christopher + Daniel + Matthew together
= 1/1451/10626
= 1 × 10626/1451 = 10626/1451 days
= 7 469/1451 days = or 7.323 days
Thus, Christopher, Daniel, and Matthew working together will finish the total work (1 work) in 7 469/1451 days = or 7.323 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 Christopher = 21 days
And the number of days required to finish the same work by Daniel = 22 days
And the number of days required to finish the work by Matthew = 23 days
Thus, the number of days required to finish the work by Christopher, Daniel, and Matthew together = ?
Here a = 21 days
And, b = 22 days
And, c = 23 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Christopher, Daniel, and Matthew working together
= 21 × 22 × 23/21 × 22 + 21 × 23 + 22 × 23 days
= 10626/462 + 483 + 506 days
= 10626/1451 days
= 10626/1451 days
= 7 469/1451 days or 7.323
Thus, Christopher, Daniel, and Matthew together will finish the work in 7 469/1451 days or 7.323 days Answer
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