Question : Joseph can finish a work in 19 days. Charles can finish the same work in 24 days while Christopher can finish the work in 29 days. How long will it take to finish it if they work together?
Correct Answer 7 1303/1703 days or 7.765 days
Solution & Explanation
Solution
Given,
The number of days required to finish a piece of work by Joseph = 19 days
And, the number of days required to finish the same work by Charles = 24 days
And, the number of days required to finish the same work by Christopher = 29 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 Joseph = 1
∴ The work done by Joseph in 1 day = 1/19
Similarly,
∵ In 24 days the work is done by Charles = 1
∴ The work done by Charles in 1 day = 1/24
Similarly,
∵ In 29 days the work is done by Christopher = 1
∴ The work done by Christopher in 1 day = 1/29 part
Now, the work done by Joseph, Charles, and Christopher together in 1 day
= Joseph's 1 day work + Charles's 1 day work + Christopher's 1 day work
= 1/19 + 1/24 + 1/29
= 696 + 551 + 456/13224
= 1703/13224 part of work
This means in 1 day, 1703/13224 part of work is done by Joseph, Charles and Christopher working together.
Now, the number of days required to finish 1703/13224 part of work by Joseph, Charles, and Christopher working together = 1
∴ the number of days required to finish the whole work (1 work) by Joseph + Charles + Christopher together
= 1/1703/13224
= 1 × 13224/1703 = 13224/1703 days
= 7 1303/1703 days = or 7.765 days
Thus, Joseph, Charles, and Christopher working together will finish the total work (1 work) in 7 1303/1703 days = or 7.765 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 Joseph = 19 days
And the number of days required to finish the same work by Charles = 24 days
And the number of days required to finish the work by Christopher = 29 days
Thus, the number of days required to finish the work by Joseph, Charles, and Christopher together = ?
Here a = 19 days
And, b = 24 days
And, c = 29 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Joseph, Charles, and Christopher working together
= 19 × 24 × 29/19 × 24 + 19 × 29 + 24 × 29 days
= 13224/456 + 551 + 696 days
= 13224/1703 days
= 13224/1703 days
= 7 1303/1703 days or 7.765
Thus, Joseph, Charles, and Christopher together will finish the work in 7 1303/1703 days or 7.765 days Answer
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