Question:
Nancy can finish a work in 28 days. Margaret can finish the same work in 33 days while Sandra can finish the work in 38 days. How long will it take to finish it if they work together?
Correct Answer
10 1346/1621 days or 10.83 days
Solution And Explanation
Solution
Given,
The number of days required to finish a piece of work by Nancy = 28 days
And, the number of days required to finish the same work by Margaret = 33 days
And, the number of days required to finish the same work by Sandra = 38 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 28 days the work is done by Nancy = 1
∴ The work done by Nancy in 1 day = 1/28
Similarly,
∵ In 33 days the work is done by Margaret = 1
∴ The work done by Margaret in 1 day = 1/33
Similarly,
∵ In 38 days the work is done by Sandra = 1
∴ The work done by Sandra in 1 day = 1/38 part
Now, the work done by Nancy, Margaret, and Sandra together in 1 day
= Nancy's 1 day work + Margaret's 1 day work + Sandra's 1 day work
= 1/28 + 1/33 + 1/38
= 627 + 532 + 462/17556
= 1621/17556 part of work
This means in 1 day, 1621/17556 part of work is done by Nancy, Margaret and Sandra working together.
Now, the number of days required to finish 1621/17556 part of work by Nancy, Margaret, and Sandra working together = 1
∴ the number of days required to finish the whole work (1 work) by Nancy + Margaret + Sandra together
= 1/1621/17556
= 1 × 17556/1621 = 17556/1621 days
= 10 1346/1621 days = or 10.83 days
Thus, Nancy, Margaret, and Sandra working together will finish the total work (1 work) in 10 1346/1621 days = or 10.83 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 Nancy = 28 days
And the number of days required to finish the same work by Margaret = 33 days
And the number of days required to finish the work by Sandra = 38 days
Thus, the number of days required to finish the work by Nancy, Margaret, and Sandra together = ?
Here a = 28 days
And, b = 33 days
And, c = 38 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Nancy, Margaret, and Sandra working together
= 28 × 33 × 38/28 × 33 + 28 × 38 + 33 × 38 days
= 35112/924 + 1064 + 1254 days
= 35112/3242 days
= 35112/3242 days
= 35112 ÷ 2/3242 ÷ 2 = 17556/1621 days
= 10 1346/1621 days or 10.83
Thus, Nancy, Margaret, and Sandra together will finish the work in 10 1346/1621 days or 10.83 days Answer
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