Question : Andrew can finish a work in 41 days. Kenneth can finish the same work in 46 days while Kevin can finish the work in 51 days. How long will it take to finish it if they work together?
Correct Answer 15 1341/6323 days or 15.212 days
Solution & Explanation
Solution
Given,
The number of days required to finish a piece of work by Andrew = 41 days
And, the number of days required to finish the same work by Kenneth = 46 days
And, the number of days required to finish the same work by Kevin = 51 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 41 days the work is done by Andrew = 1
∴ The work done by Andrew in 1 day = 1/41
Similarly,
∵ In 46 days the work is done by Kenneth = 1
∴ The work done by Kenneth in 1 day = 1/46
Similarly,
∵ In 51 days the work is done by Kevin = 1
∴ The work done by Kevin in 1 day = 1/51 part
Now, the work done by Andrew, Kenneth, and Kevin together in 1 day
= Andrew's 1 day work + Kenneth's 1 day work + Kevin's 1 day work
= 1/41 + 1/46 + 1/51
= 2346 + 2091 + 1886/96186
= 6323/96186 part of work
This means in 1 day, 6323/96186 part of work is done by Andrew, Kenneth and Kevin working together.
Now, the number of days required to finish 6323/96186 part of work by Andrew, Kenneth, and Kevin working together = 1
∴ the number of days required to finish the whole work (1 work) by Andrew + Kenneth + Kevin together
= 1/6323/96186
= 1 × 96186/6323 = 96186/6323 days
= 15 1341/6323 days = or 15.212 days
Thus, Andrew, Kenneth, and Kevin working together will finish the total work (1 work) in 15 1341/6323 days = or 15.212 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 Andrew = 41 days
And the number of days required to finish the same work by Kenneth = 46 days
And the number of days required to finish the work by Kevin = 51 days
Thus, the number of days required to finish the work by Andrew, Kenneth, and Kevin together = ?
Here a = 41 days
And, b = 46 days
And, c = 51 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Andrew, Kenneth, and Kevin working together
= 41 × 46 × 51/41 × 46 + 41 × 51 + 46 × 51 days
= 96186/1886 + 2091 + 2346 days
= 96186/6323 days
= 96186/6323 days
= 15 1341/6323 days or 15.212
Thus, Andrew, Kenneth, and Kevin together will finish the work in 15 1341/6323 days or 15.212 days Answer
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