Question:
Nancy can finish a work in 24 days. Betty can finish the same work in 25 days while Margaret can finish the work in 26 days. How long will it take to finish it if they work together?
Correct Answer
8 304/937 days or 8.324 days
Solution And Explanation
Solution
Given,
The number of days required to finish a piece of work by Nancy = 24 days
And, the number of days required to finish the same work by Betty = 25 days
And, the number of days required to finish the same work by Margaret = 26 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 Nancy = 1
∴ The work done by Nancy in 1 day = 1/24
Similarly,
∵ In 25 days the work is done by Betty = 1
∴ The work done by Betty in 1 day = 1/25
Similarly,
∵ In 26 days the work is done by Margaret = 1
∴ The work done by Margaret in 1 day = 1/26 part
Now, the work done by Nancy, Betty, and Margaret together in 1 day
= Nancy's 1 day work + Betty's 1 day work + Margaret's 1 day work
= 1/24 + 1/25 + 1/26
= 325 + 312 + 300/7800
= 937/7800 part of work
This means in 1 day, 937/7800 part of work is done by Nancy, Betty and Margaret working together.
Now, the number of days required to finish 937/7800 part of work by Nancy, Betty, and Margaret working together = 1
∴ the number of days required to finish the whole work (1 work) by Nancy + Betty + Margaret together
= 1/937/7800
= 1 × 7800/937 = 7800/937 days
= 8 304/937 days = or 8.324 days
Thus, Nancy, Betty, and Margaret working together will finish the total work (1 work) in 8 304/937 days = or 8.324 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 = 24 days
And the number of days required to finish the same work by Betty = 25 days
And the number of days required to finish the work by Margaret = 26 days
Thus, the number of days required to finish the work by Nancy, Betty, and Margaret together = ?
Here a = 24 days
And, b = 25 days
And, c = 26 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Nancy, Betty, and Margaret working together
= 24 × 25 × 26/24 × 25 + 24 × 26 + 25 × 26 days
= 15600/600 + 624 + 650 days
= 15600/1874 days
= 15600/1874 days
= 15600 ÷ 2/1874 ÷ 2 = 7800/937 days
= 8 304/937 days or 8.324
Thus, Nancy, Betty, and Margaret together will finish the work in 8 304/937 days or 8.324 days Answer
Similar Questions
(1) Emily can finish a work in 40 days. Michelle can finish the same work in 45 days while Carol can finish the work in 50 days. How long will it take to finish it if they work together?
(2) Andrew can finish a work in 41 days. Kenneth can finish the same work in 46 days while Kevin can finish the work in 51 days. How long will it take to finish it if they work together?
(3) Mark can finish a work in 29 days. Donald can finish the same work in 30 days while Steven can finish the work in 31 days. How long will it take to finish it if they work together?
(4) If John can finish the work in 28 days and Richard can finish the same work in 44 days, then in how many days both can finish the work together?
(5) If Matthew can finish the work in 26 days and Edward can finish the same work in 29 days, then in how many days both can finish the work together?
(6) Amanda can finish a work in 48 days. Melissa can finish the same work in 53 days while Deborah can finish the work in 58 days. How long will it take to finish it if they work together?
(7) Joseph can finish a work in 15 days. Thomas can finish the same work in 16 days while Charles can finish the work in 17 days. How long will it take to finish it if they work together?
(8) Kimberly can finish a work in 34 days. Emily can finish the same work in 35 days while Donna can finish the work in 36 days. How long will it take to finish it if they work together?
(9) Christopher can finish a work in 25 days. Matthew can finish the same work in 30 days while Anthony can finish the work in 35 days. How long will it take to finish it if they work together?
(10) If Eric can finish the work in 71 days and Gerald can finish the same work in 76 days, then in how many days both can finish the work together?