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 & 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
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