Question:
Charles can finish a work in 19 days. Christopher can finish the same work in 20 days while Daniel can finish the work in 21 days. How long will it take to finish it if they work together?
Correct Answer
6 786/1199 days or 6.656 days
Solution And Explanation
Solution
Given,
The number of days required to finish a piece of work by Charles = 19 days
And, the number of days required to finish the same work by Christopher = 20 days
And, the number of days required to finish the same work by Daniel = 21 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 19 days the work is done by Charles = 1
∴ The work done by Charles in 1 day = 1/19
Similarly,
∵ In 20 days the work is done by Christopher = 1
∴ The work done by Christopher in 1 day = 1/20
Similarly,
∵ In 21 days the work is done by Daniel = 1
∴ The work done by Daniel in 1 day = 1/21 part
Now, the work done by Charles, Christopher, and Daniel together in 1 day
= Charles's 1 day work + Christopher's 1 day work + Daniel's 1 day work
= 1/19 + 1/20 + 1/21
= 420 + 399 + 380/7980
= 1199/7980 part of work
This means in 1 day, 1199/7980 part of work is done by Charles, Christopher and Daniel working together.
Now, the number of days required to finish 1199/7980 part of work by Charles, Christopher, and Daniel working together = 1
∴ the number of days required to finish the whole work (1 work) by Charles + Christopher + Daniel together
= 1/1199/7980
= 1 × 7980/1199 = 7980/1199 days
= 6 786/1199 days = or 6.656 days
Thus, Charles, Christopher, and Daniel working together will finish the total work (1 work) in 6 786/1199 days = or 6.656 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 = 19 days
And the number of days required to finish the same work by Christopher = 20 days
And the number of days required to finish the work by Daniel = 21 days
Thus, the number of days required to finish the work by Charles, Christopher, and Daniel together = ?
Here a = 19 days
And, b = 20 days
And, c = 21 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Charles, Christopher, and Daniel working together
= 19 × 20 × 21/19 × 20 + 19 × 21 + 20 × 21 days
= 7980/380 + 399 + 420 days
= 7980/1199 days
= 7980/1199 days
= 6 786/1199 days or 6.656
Thus, Charles, Christopher, and Daniel together will finish the work in 6 786/1199 days or 6.656 days Answer
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