Question:
Thomas can finish a work in 21 days. Christopher can finish the same work in 26 days while Daniel can finish the work in 31 days. How long will it take to finish it if they work together?
Correct Answer
8 902/2003 days or 8.45 days
Solution And Explanation
Solution
Given,
The number of days required to finish a piece of work by Thomas = 21 days
And, the number of days required to finish the same work by Christopher = 26 days
And, the number of days required to finish the same work by Daniel = 31 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 Thomas = 1
∴ The work done by Thomas in 1 day = 1/21
Similarly,
∵ In 26 days the work is done by Christopher = 1
∴ The work done by Christopher in 1 day = 1/26
Similarly,
∵ In 31 days the work is done by Daniel = 1
∴ The work done by Daniel in 1 day = 1/31 part
Now, the work done by Thomas, Christopher, and Daniel together in 1 day
= Thomas's 1 day work + Christopher's 1 day work + Daniel's 1 day work
= 1/21 + 1/26 + 1/31
= 806 + 651 + 546/16926
= 2003/16926 part of work
This means in 1 day, 2003/16926 part of work is done by Thomas, Christopher and Daniel working together.
Now, the number of days required to finish 2003/16926 part of work by Thomas, Christopher, and Daniel working together = 1
∴ the number of days required to finish the whole work (1 work) by Thomas + Christopher + Daniel together
= 1/2003/16926
= 1 × 16926/2003 = 16926/2003 days
= 8 902/2003 days = or 8.45 days
Thus, Thomas, Christopher, and Daniel working together will finish the total work (1 work) in 8 902/2003 days = or 8.45 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 Thomas = 21 days
And the number of days required to finish the same work by Christopher = 26 days
And the number of days required to finish the work by Daniel = 31 days
Thus, the number of days required to finish the work by Thomas, Christopher, and Daniel together = ?
Here a = 21 days
And, b = 26 days
And, c = 31 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Thomas, Christopher, and Daniel working together
= 21 × 26 × 31/21 × 26 + 21 × 31 + 26 × 31 days
= 16926/546 + 651 + 806 days
= 16926/2003 days
= 16926/2003 days
= 8 902/2003 days or 8.45
Thus, Thomas, Christopher, and Daniel together will finish the work in 8 902/2003 days or 8.45 days Answer
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