Question:
Lisa can finish a work in 26 days. Betty can finish the same work in 31 days while Margaret can finish the work in 36 days. How long will it take to finish it if they work together?
Correct Answer
10 218/1429 days or 10.153 days
Solution And Explanation
Solution
Given,
The number of days required to finish a piece of work by Lisa = 26 days
And, the number of days required to finish the same work by Betty = 31 days
And, the number of days required to finish the same work by Margaret = 36 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 26 days the work is done by Lisa = 1
∴ The work done by Lisa in 1 day = 1/26
Similarly,
∵ In 31 days the work is done by Betty = 1
∴ The work done by Betty in 1 day = 1/31
Similarly,
∵ In 36 days the work is done by Margaret = 1
∴ The work done by Margaret in 1 day = 1/36 part
Now, the work done by Lisa, Betty, and Margaret together in 1 day
= Lisa's 1 day work + Betty's 1 day work + Margaret's 1 day work
= 1/26 + 1/31 + 1/36
= 558 + 468 + 403/14508
= 1429/14508 part of work
This means in 1 day, 1429/14508 part of work is done by Lisa, Betty and Margaret working together.
Now, the number of days required to finish 1429/14508 part of work by Lisa, Betty, and Margaret working together = 1
∴ the number of days required to finish the whole work (1 work) by Lisa + Betty + Margaret together
= 1/1429/14508
= 1 × 14508/1429 = 14508/1429 days
= 10 218/1429 days = or 10.153 days
Thus, Lisa, Betty, and Margaret working together will finish the total work (1 work) in 10 218/1429 days = or 10.153 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 = 26 days
And the number of days required to finish the same work by Betty = 31 days
And the number of days required to finish the work by Margaret = 36 days
Thus, the number of days required to finish the work by Lisa, Betty, and Margaret together = ?
Here a = 26 days
And, b = 31 days
And, c = 36 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Lisa, Betty, and Margaret working together
= 26 × 31 × 36/26 × 31 + 26 × 36 + 31 × 36 days
= 29016/806 + 936 + 1116 days
= 29016/2858 days
= 29016/2858 days
= 29016 ÷ 2/2858 ÷ 2 = 14508/1429 days
= 10 218/1429 days or 10.153
Thus, Lisa, Betty, and Margaret together will finish the work in 10 218/1429 days or 10.153 days Answer
Similar Questions
(1) If David can finish the work in 32 days and Christopher can finish the same work in 48 days, then in how many days both can finish the work together?
(2) Dorothy can finish a work in 50 days. Deborah can finish the same work in 55 days while Stephanie can finish the work in 60 days. How long will it take to finish it if they work together?
(3) Betty can finish a work in 30 days. Sandra can finish the same work in 35 days while Ashley can finish the work in 40 days. How long will it take to finish it if they work together?
(4) If Helen can finish the work in 84 days and Bruce can finish the same work in 89 days, then in how many days both can finish the work together?
(5) If Robert can finish a work in 4 days and Bob can finish the same work in 6 days, then in how many days they both can finish the work working together?
(6) Dorothy can finish a work in 46 days. Melissa can finish the same work in 47 days while Deborah can finish the work in 48 days. How long will it take to finish it if they work together?
(7) If Sandra can finish the work in 31 days and Gary can finish the same work in 34 days, then in how many days both can finish the work together?
(8) If Steven can finish the work in 34 days and Jonathan can finish the same work in 38 days, then in how many days both can finish the work together?
(9) Kenneth can finish a work in 45 days. Brian can finish the same work in 50 days while George can finish the work in 55 days. How long will it take to finish it if they work together?
(10) If Larry can finish the work in 77 days and Lawrence can finish the same work in 82 days, then in how many days both can finish the work together?