Question : Thomas can finish a work in 17 days. Charles can finish the same work in 18 days while Christopher can finish the work in 19 days. How long will it take to finish it if they work together?
Correct Answer 5 959/971 days or 5.988 days
Solution & Explanation
Solution
Given,
The number of days required to finish a piece of work by Thomas = 17 days
And, the number of days required to finish the same work by Charles = 18 days
And, the number of days required to finish the same work by Christopher = 19 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 17 days the work is done by Thomas = 1
∴ The work done by Thomas in 1 day = 1/17
Similarly,
∵ In 18 days the work is done by Charles = 1
∴ The work done by Charles in 1 day = 1/18
Similarly,
∵ In 19 days the work is done by Christopher = 1
∴ The work done by Christopher in 1 day = 1/19 part
Now, the work done by Thomas, Charles, and Christopher together in 1 day
= Thomas's 1 day work + Charles's 1 day work + Christopher's 1 day work
= 1/17 + 1/18 + 1/19
= 342 + 323 + 306/5814
= 971/5814 part of work
This means in 1 day, 971/5814 part of work is done by Thomas, Charles and Christopher working together.
Now, the number of days required to finish 971/5814 part of work by Thomas, Charles, and Christopher working together = 1
∴ the number of days required to finish the whole work (1 work) by Thomas + Charles + Christopher together
= 1/971/5814
= 1 × 5814/971 = 5814/971 days
= 5 959/971 days = or 5.988 days
Thus, Thomas, Charles, and Christopher working together will finish the total work (1 work) in 5 959/971 days = or 5.988 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 = 17 days
And the number of days required to finish the same work by Charles = 18 days
And the number of days required to finish the work by Christopher = 19 days
Thus, the number of days required to finish the work by Thomas, Charles, and Christopher together = ?
Here a = 17 days
And, b = 18 days
And, c = 19 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Thomas, Charles, and Christopher working together
= 17 × 18 × 19/17 × 18 + 17 × 19 + 18 × 19 days
= 5814/306 + 323 + 342 days
= 5814/971 days
= 5814/971 days
= 5 959/971 days or 5.988
Thus, Thomas, Charles, and Christopher together will finish the work in 5 959/971 days or 5.988 days Answer
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