Question:
Betty can finish a work in 26 days. Margaret can finish the same work in 27 days while Sandra can finish the work in 28 days. How long will it take to finish it if they work together?
Correct Answer
8 1084/1093 days or 8.992 days
Solution And Explanation
Solution
Given,
The number of days required to finish a piece of work by Betty = 26 days
And, the number of days required to finish the same work by Margaret = 27 days
And, the number of days required to finish the same work by Sandra = 28 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 26 days the work is done by Betty = 1
∴ The work done by Betty in 1 day = 1/26
Similarly,
∵ In 27 days the work is done by Margaret = 1
∴ The work done by Margaret in 1 day = 1/27
Similarly,
∵ In 28 days the work is done by Sandra = 1
∴ The work done by Sandra in 1 day = 1/28 part
Now, the work done by Betty, Margaret, and Sandra together in 1 day
= Betty's 1 day work + Margaret's 1 day work + Sandra's 1 day work
= 1/26 + 1/27 + 1/28
= 378 + 364 + 351/9828
= 1093/9828 part of work
This means in 1 day, 1093/9828 part of work is done by Betty, Margaret and Sandra working together.
Now, the number of days required to finish 1093/9828 part of work by Betty, Margaret, and Sandra working together = 1
∴ the number of days required to finish the whole work (1 work) by Betty + Margaret + Sandra together
= 1/1093/9828
= 1 × 9828/1093 = 9828/1093 days
= 8 1084/1093 days = or 8.992 days
Thus, Betty, Margaret, and Sandra working together will finish the total work (1 work) in 8 1084/1093 days = or 8.992 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 Betty = 26 days
And the number of days required to finish the same work by Margaret = 27 days
And the number of days required to finish the work by Sandra = 28 days
Thus, the number of days required to finish the work by Betty, Margaret, and Sandra together = ?
Here a = 26 days
And, b = 27 days
And, c = 28 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Betty, Margaret, and Sandra working together
= 26 × 27 × 28/26 × 27 + 26 × 28 + 27 × 28 days
= 19656/702 + 728 + 756 days
= 19656/2186 days
= 19656/2186 days
= 19656 ÷ 2/2186 ÷ 2 = 9828/1093 days
= 8 1084/1093 days or 8.992
Thus, Betty, Margaret, and Sandra together will finish the work in 8 1084/1093 days or 8.992 days Answer
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