Question:
Lisa can finish a work in 22 days. Nancy can finish the same work in 23 days while Betty can finish the work in 24 days. How long will it take to finish it if they work together?
Correct Answer
7 521/793 days or 7.657 days
Solution And Explanation
Solution
Given,
The number of days required to finish a piece of work by Lisa = 22 days
And, the number of days required to finish the same work by Nancy = 23 days
And, the number of days required to finish the same work by Betty = 24 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 22 days the work is done by Lisa = 1
∴ The work done by Lisa in 1 day = 1/22
Similarly,
∵ In 23 days the work is done by Nancy = 1
∴ The work done by Nancy in 1 day = 1/23
Similarly,
∵ In 24 days the work is done by Betty = 1
∴ The work done by Betty in 1 day = 1/24 part
Now, the work done by Lisa, Nancy, and Betty together in 1 day
= Lisa's 1 day work + Nancy's 1 day work + Betty's 1 day work
= 1/22 + 1/23 + 1/24
= 276 + 264 + 253/6072
= 793/6072 part of work
This means in 1 day, 793/6072 part of work is done by Lisa, Nancy and Betty working together.
Now, the number of days required to finish 793/6072 part of work by Lisa, Nancy, and Betty working together = 1
∴ the number of days required to finish the whole work (1 work) by Lisa + Nancy + Betty together
= 1/793/6072
= 1 × 6072/793 = 6072/793 days
= 7 521/793 days = or 7.657 days
Thus, Lisa, Nancy, and Betty working together will finish the total work (1 work) in 7 521/793 days = or 7.657 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 Lisa = 22 days
And the number of days required to finish the same work by Nancy = 23 days
And the number of days required to finish the work by Betty = 24 days
Thus, the number of days required to finish the work by Lisa, Nancy, and Betty together = ?
Here a = 22 days
And, b = 23 days
And, c = 24 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Lisa, Nancy, and Betty working together
= 22 × 23 × 24/22 × 23 + 22 × 24 + 23 × 24 days
= 12144/506 + 528 + 552 days
= 12144/1586 days
= 12144/1586 days
= 12144 ÷ 2/1586 ÷ 2 = 6072/793 days
= 7 521/793 days or 7.657
Thus, Lisa, Nancy, and Betty together will finish the work in 7 521/793 days or 7.657 days Answer
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