Question:
Charles can finish a work in 23 days. Daniel can finish the same work in 28 days while Matthew can finish the work in 33 days. How long will it take to finish it if they work together?
Correct Answer
9 309/2327 days or 9.133 days
Solution And Explanation
Solution
Given,
The number of days required to finish a piece of work by Charles = 23 days
And, the number of days required to finish the same work by Daniel = 28 days
And, the number of days required to finish the same work by Matthew = 33 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 Charles = 1
∴ The work done by Charles in 1 day = 1/23
Similarly,
∵ In 28 days the work is done by Daniel = 1
∴ The work done by Daniel in 1 day = 1/28
Similarly,
∵ In 33 days the work is done by Matthew = 1
∴ The work done by Matthew in 1 day = 1/33 part
Now, the work done by Charles, Daniel, and Matthew together in 1 day
= Charles's 1 day work + Daniel's 1 day work + Matthew's 1 day work
= 1/23 + 1/28 + 1/33
= 924 + 759 + 644/21252
= 2327/21252 part of work
This means in 1 day, 2327/21252 part of work is done by Charles, Daniel and Matthew working together.
Now, the number of days required to finish 2327/21252 part of work by Charles, Daniel, and Matthew working together = 1
∴ the number of days required to finish the whole work (1 work) by Charles + Daniel + Matthew together
= 1/2327/21252
= 1 × 21252/2327 = 21252/2327 days
= 9 309/2327 days = or 9.133 days
Thus, Charles, Daniel, and Matthew working together will finish the total work (1 work) in 9 309/2327 days = or 9.133 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 Charles = 23 days
And the number of days required to finish the same work by Daniel = 28 days
And the number of days required to finish the work by Matthew = 33 days
Thus, the number of days required to finish the work by Charles, Daniel, and Matthew together = ?
Here a = 23 days
And, b = 28 days
And, c = 33 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Charles, Daniel, and Matthew working together
= 23 × 28 × 33/23 × 28 + 23 × 33 + 28 × 33 days
= 21252/644 + 759 + 924 days
= 21252/2327 days
= 21252/2327 days
= 9 309/2327 days or 9.133
Thus, Charles, Daniel, and Matthew together will finish the work in 9 309/2327 days or 9.133 days Answer
Similar Questions
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