Question : Benjamin can finish a work in 85 days. Gregory can finish the same work in 90 days while Alexander can finish the work in 95 days. How long will it take to finish it if they work together?
Correct Answer 29 911/971 days or 29.938 days
Solution & Explanation
Solution
Given,
The number of days required to finish a piece of work by Benjamin = 85 days
And, the number of days required to finish the same work by Gregory = 90 days
And, the number of days required to finish the same work by Alexander = 95 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 85 days the work is done by Benjamin = 1
∴ The work done by Benjamin in 1 day = 1/85
Similarly,
∵ In 90 days the work is done by Gregory = 1
∴ The work done by Gregory in 1 day = 1/90
Similarly,
∵ In 95 days the work is done by Alexander = 1
∴ The work done by Alexander in 1 day = 1/95 part
Now, the work done by Benjamin, Gregory, and Alexander together in 1 day
= Benjamin's 1 day work + Gregory's 1 day work + Alexander's 1 day work
= 1/85 + 1/90 + 1/95
= 342 + 323 + 306/29070
= 971/29070 part of work
This means in 1 day, 971/29070 part of work is done by Benjamin, Gregory and Alexander working together.
Now, the number of days required to finish 971/29070 part of work by Benjamin, Gregory, and Alexander working together = 1
∴ the number of days required to finish the whole work (1 work) by Benjamin + Gregory + Alexander together
= 1/971/29070
= 1 × 29070/971 = 29070/971 days
= 29 911/971 days = or 29.938 days
Thus, Benjamin, Gregory, and Alexander working together will finish the total work (1 work) in 29 911/971 days = or 29.938 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 Benjamin = 85 days
And the number of days required to finish the same work by Gregory = 90 days
And the number of days required to finish the work by Alexander = 95 days
Thus, the number of days required to finish the work by Benjamin, Gregory, and Alexander together = ?
Here a = 85 days
And, b = 90 days
And, c = 95 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Benjamin, Gregory, and Alexander working together
= 85 × 90 × 95/85 × 90 + 85 × 95 + 90 × 95 days
= 726750/7650 + 8075 + 8550 days
= 726750/24275 days
= 726750/24275 days
= 726750 ÷ 25/24275 ÷ 25 = 29070/971 days
= 29 911/971 days or 29.938
Thus, Benjamin, Gregory, and Alexander together will finish the work in 29 911/971 days or 29.938 days Answer
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