Question:
Mark can finish a work in 33 days. Steven can finish the same work in 38 days while Paul can finish the work in 43 days. How long will it take to finish it if they work together?
Correct Answer
12 2238/4307 days or 12.52 days
Solution And Explanation
Solution
Given,
The number of days required to finish a piece of work by Mark = 33 days
And, the number of days required to finish the same work by Steven = 38 days
And, the number of days required to finish the same work by Paul = 43 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 33 days the work is done by Mark = 1
∴ The work done by Mark in 1 day = 1/33
Similarly,
∵ In 38 days the work is done by Steven = 1
∴ The work done by Steven in 1 day = 1/38
Similarly,
∵ In 43 days the work is done by Paul = 1
∴ The work done by Paul in 1 day = 1/43 part
Now, the work done by Mark, Steven, and Paul together in 1 day
= Mark's 1 day work + Steven's 1 day work + Paul's 1 day work
= 1/33 + 1/38 + 1/43
= 1634 + 1419 + 1254/53922
= 4307/53922 part of work
This means in 1 day, 4307/53922 part of work is done by Mark, Steven and Paul working together.
Now, the number of days required to finish 4307/53922 part of work by Mark, Steven, and Paul working together = 1
∴ the number of days required to finish the whole work (1 work) by Mark + Steven + Paul together
= 1/4307/53922
= 1 × 53922/4307 = 53922/4307 days
= 12 2238/4307 days = or 12.52 days
Thus, Mark, Steven, and Paul working together will finish the total work (1 work) in 12 2238/4307 days = or 12.52 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 Mark = 33 days
And the number of days required to finish the same work by Steven = 38 days
And the number of days required to finish the work by Paul = 43 days
Thus, the number of days required to finish the work by Mark, Steven, and Paul together = ?
Here a = 33 days
And, b = 38 days
And, c = 43 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Mark, Steven, and Paul working together
= 33 × 38 × 43/33 × 38 + 33 × 43 + 38 × 43 days
= 53922/1254 + 1419 + 1634 days
= 53922/4307 days
= 53922/4307 days
= 12 2238/4307 days or 12.52
Thus, Mark, Steven, and Paul together will finish the work in 12 2238/4307 days or 12.52 days Answer
Similar Questions
(1) If Ashley can finish the work in 33 days and Eric can finish the same work in 37 days, then in how many days both can finish the work together?
(2) If Joshua can finish the work in 40 days and Benjamin can finish the same work in 43 days, then in how many days both can finish the work together?
(3) Samantha can finish a work in 86 days. Christine can finish the same work in 91 days while Debra can finish the work in 96 days. How long will it take to finish it if they work together?
(4) Daniel can finish a work in 23 days. Matthew can finish the same work in 24 days while Anthony can finish the work in 25 days. How long will it take to finish it if they work together?
(5) If Patricia can finish the work in 27 days and William can finish the same work in 43 days, then in how many days both can finish the work together?
(6) Timothy can finish a work in 53 days. Edward can finish the same work in 58 days while Jason can finish the work in 63 days. How long will it take to finish it if they work together?
(7) If Melissa can finish the work in 52 days and Jerry can finish the same work in 57 days, then in how many days both can finish the work together?
(8) If Deborah can finish the work in 54 days and Aaron can finish the same work in 59 days, then in how many days both can finish the work together?
(9) Carol can finish a work in 46 days. Dorothy can finish the same work in 51 days while Melissa can finish the work in 56 days. How long will it take to finish it if they work together?
(10) Deborah can finish a work in 50 days. Stephanie can finish the same work in 51 days while Rebecca can finish the work in 52 days. How long will it take to finish it if they work together?