Question : Kenneth can finish a work in 45 days. Brian can finish the same work in 50 days while George can finish the work in 55 days. How long will it take to finish it if they work together?
Correct Answer 16 166/299 days or 16.555 days
Solution & Explanation
Solution
Given,
The number of days required to finish a piece of work by Kenneth = 45 days
And, the number of days required to finish the same work by Brian = 50 days
And, the number of days required to finish the same work by George = 55 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 45 days the work is done by Kenneth = 1
∴ The work done by Kenneth in 1 day = 1/45
Similarly,
∵ In 50 days the work is done by Brian = 1
∴ The work done by Brian in 1 day = 1/50
Similarly,
∵ In 55 days the work is done by George = 1
∴ The work done by George in 1 day = 1/55 part
Now, the work done by Kenneth, Brian, and George together in 1 day
= Kenneth's 1 day work + Brian's 1 day work + George's 1 day work
= 1/45 + 1/50 + 1/55
= 110 + 99 + 90/4950
= 299/4950 part of work
This means in 1 day, 299/4950 part of work is done by Kenneth, Brian and George working together.
Now, the number of days required to finish 299/4950 part of work by Kenneth, Brian, and George working together = 1
∴ the number of days required to finish the whole work (1 work) by Kenneth + Brian + George together
= 1/299/4950
= 1 × 4950/299 = 4950/299 days
= 16 166/299 days = or 16.555 days
Thus, Kenneth, Brian, and George working together will finish the total work (1 work) in 16 166/299 days = or 16.555 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 Kenneth = 45 days
And the number of days required to finish the same work by Brian = 50 days
And the number of days required to finish the work by George = 55 days
Thus, the number of days required to finish the work by Kenneth, Brian, and George together = ?
Here a = 45 days
And, b = 50 days
And, c = 55 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Kenneth, Brian, and George working together
= 45 × 50 × 55/45 × 50 + 45 × 55 + 50 × 55 days
= 123750/2250 + 2475 + 2750 days
= 123750/7475 days
= 123750/7475 days
= 123750 ÷ 25/7475 ÷ 25 = 4950/299 days
= 16 166/299 days or 16.555
Thus, Kenneth, Brian, and George together will finish the work in 16 166/299 days or 16.555 days Answer
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