Question : Elizabeth can finish a work in 10 days. Barbara can finish the same work in 11 days while Susan can finish the work in 12 days. How long will it take to finish it if they work together?
Correct Answer 3 117/181 days or 3.646 days
Solution & Explanation
Solution
Given,
The number of days required to finish a piece of work by Elizabeth = 10 days
And, the number of days required to finish the same work by Barbara = 11 days
And, the number of days required to finish the same work by Susan = 12 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 10 days the work is done by Elizabeth = 1
∴ The work done by Elizabeth in 1 day = 1/10
Similarly,
∵ In 11 days the work is done by Barbara = 1
∴ The work done by Barbara in 1 day = 1/11
Similarly,
∵ In 12 days the work is done by Susan = 1
∴ The work done by Susan in 1 day = 1/12 part
Now, the work done by Elizabeth, Barbara, and Susan together in 1 day
= Elizabeth's 1 day work + Barbara's 1 day work + Susan's 1 day work
= 1/10 + 1/11 + 1/12
= 66 + 60 + 55/660
= 181/660 part of work
This means in 1 day, 181/660 part of work is done by Elizabeth, Barbara and Susan working together.
Now, the number of days required to finish 181/660 part of work by Elizabeth, Barbara, and Susan working together = 1
∴ the number of days required to finish the whole work (1 work) by Elizabeth + Barbara + Susan together
= 1/181/660
= 1 × 660/181 = 660/181 days
= 3 117/181 days = or 3.646 days
Thus, Elizabeth, Barbara, and Susan working together will finish the total work (1 work) in 3 117/181 days = or 3.646 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 Elizabeth = 10 days
And the number of days required to finish the same work by Barbara = 11 days
And the number of days required to finish the work by Susan = 12 days
Thus, the number of days required to finish the work by Elizabeth, Barbara, and Susan together = ?
Here a = 10 days
And, b = 11 days
And, c = 12 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Elizabeth, Barbara, and Susan working together
= 10 × 11 × 12/10 × 11 + 10 × 12 + 11 × 12 days
= 1320/110 + 120 + 132 days
= 1320/362 days
= 1320/362 days
= 1320 ÷ 2/362 ÷ 2 = 660/181 days
= 3 117/181 days or 3.646
Thus, Elizabeth, Barbara, and Susan together will finish the work in 3 117/181 days or 3.646 days Answer
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