Question : Anthony can finish a work in 31 days. Donald can finish the same work in 36 days while Steven can finish the work in 41 days. How long will it take to finish it if they work together?
Correct Answer 11 3263/3863 days or 11.845 days
Solution & Explanation
Solution
Given,
The number of days required to finish a piece of work by Anthony = 31 days
And, the number of days required to finish the same work by Donald = 36 days
And, the number of days required to finish the same work by Steven = 41 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 31 days the work is done by Anthony = 1
∴ The work done by Anthony in 1 day = 1/31
Similarly,
∵ In 36 days the work is done by Donald = 1
∴ The work done by Donald in 1 day = 1/36
Similarly,
∵ In 41 days the work is done by Steven = 1
∴ The work done by Steven in 1 day = 1/41 part
Now, the work done by Anthony, Donald, and Steven together in 1 day
= Anthony's 1 day work + Donald's 1 day work + Steven's 1 day work
= 1/31 + 1/36 + 1/41
= 1476 + 1271 + 1116/45756
= 3863/45756 part of work
This means in 1 day, 3863/45756 part of work is done by Anthony, Donald and Steven working together.
Now, the number of days required to finish 3863/45756 part of work by Anthony, Donald, and Steven working together = 1
∴ the number of days required to finish the whole work (1 work) by Anthony + Donald + Steven together
= 1/3863/45756
= 1 × 45756/3863 = 45756/3863 days
= 11 3263/3863 days = or 11.845 days
Thus, Anthony, Donald, and Steven working together will finish the total work (1 work) in 11 3263/3863 days = or 11.845 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 Anthony = 31 days
And the number of days required to finish the same work by Donald = 36 days
And the number of days required to finish the work by Steven = 41 days
Thus, the number of days required to finish the work by Anthony, Donald, and Steven together = ?
Here a = 31 days
And, b = 36 days
And, c = 41 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Anthony, Donald, and Steven working together
= 31 × 36 × 41/31 × 36 + 31 × 41 + 36 × 41 days
= 45756/1116 + 1271 + 1476 days
= 45756/3863 days
= 45756/3863 days
= 11 3263/3863 days or 11.845
Thus, Anthony, Donald, and Steven together will finish the work in 11 3263/3863 days or 11.845 days Answer
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