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 & 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
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