Question:
Karen can finish a work in 24 days. Nancy can finish the same work in 29 days while Betty can finish the work in 34 days. How long will it take to finish it if they work together?
Correct Answer
9 591/1249 days or 9.473 days
Solution And Explanation
Solution
Given,
The number of days required to finish a piece of work by Karen = 24 days
And, the number of days required to finish the same work by Nancy = 29 days
And, the number of days required to finish the same work by Betty = 34 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 24 days the work is done by Karen = 1
∴ The work done by Karen in 1 day = 1/24
Similarly,
∵ In 29 days the work is done by Nancy = 1
∴ The work done by Nancy in 1 day = 1/29
Similarly,
∵ In 34 days the work is done by Betty = 1
∴ The work done by Betty in 1 day = 1/34 part
Now, the work done by Karen, Nancy, and Betty together in 1 day
= Karen's 1 day work + Nancy's 1 day work + Betty's 1 day work
= 1/24 + 1/29 + 1/34
= 493 + 408 + 348/11832
= 1249/11832 part of work
This means in 1 day, 1249/11832 part of work is done by Karen, Nancy and Betty working together.
Now, the number of days required to finish 1249/11832 part of work by Karen, Nancy, and Betty working together = 1
∴ the number of days required to finish the whole work (1 work) by Karen + Nancy + Betty together
= 1/1249/11832
= 1 × 11832/1249 = 11832/1249 days
= 9 591/1249 days = or 9.473 days
Thus, Karen, Nancy, and Betty working together will finish the total work (1 work) in 9 591/1249 days = or 9.473 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 Karen = 24 days
And the number of days required to finish the same work by Nancy = 29 days
And the number of days required to finish the work by Betty = 34 days
Thus, the number of days required to finish the work by Karen, Nancy, and Betty together = ?
Here a = 24 days
And, b = 29 days
And, c = 34 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Karen, Nancy, and Betty working together
= 24 × 29 × 34/24 × 29 + 24 × 34 + 29 × 34 days
= 23664/696 + 816 + 986 days
= 23664/2498 days
= 23664/2498 days
= 23664 ÷ 2/2498 ÷ 2 = 11832/1249 days
= 9 591/1249 days or 9.473
Thus, Karen, Nancy, and Betty together will finish the work in 9 591/1249 days or 9.473 days Answer
Similar Questions
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