Question:
Steven can finish a work in 33 days. Paul can finish the same work in 34 days while Andrew can finish the work in 35 days. How long will it take to finish it if they work together?
Correct Answer
11 1133/3467 days or 11.327 days
Solution And Explanation
Solution
Given,
The number of days required to finish a piece of work by Steven = 33 days
And, the number of days required to finish the same work by Paul = 34 days
And, the number of days required to finish the same work by Andrew = 35 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 Steven = 1
∴ The work done by Steven in 1 day = 1/33
Similarly,
∵ In 34 days the work is done by Paul = 1
∴ The work done by Paul in 1 day = 1/34
Similarly,
∵ In 35 days the work is done by Andrew = 1
∴ The work done by Andrew in 1 day = 1/35 part
Now, the work done by Steven, Paul, and Andrew together in 1 day
= Steven's 1 day work + Paul's 1 day work + Andrew's 1 day work
= 1/33 + 1/34 + 1/35
= 1190 + 1155 + 1122/39270
= 3467/39270 part of work
This means in 1 day, 3467/39270 part of work is done by Steven, Paul and Andrew working together.
Now, the number of days required to finish 3467/39270 part of work by Steven, Paul, and Andrew working together = 1
∴ the number of days required to finish the whole work (1 work) by Steven + Paul + Andrew together
= 1/3467/39270
= 1 × 39270/3467 = 39270/3467 days
= 11 1133/3467 days = or 11.327 days
Thus, Steven, Paul, and Andrew working together will finish the total work (1 work) in 11 1133/3467 days = or 11.327 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 Steven = 33 days
And the number of days required to finish the same work by Paul = 34 days
And the number of days required to finish the work by Andrew = 35 days
Thus, the number of days required to finish the work by Steven, Paul, and Andrew together = ?
Here a = 33 days
And, b = 34 days
And, c = 35 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Steven, Paul, and Andrew working together
= 33 × 34 × 35/33 × 34 + 33 × 35 + 34 × 35 days
= 39270/1122 + 1155 + 1190 days
= 39270/3467 days
= 39270/3467 days
= 11 1133/3467 days or 11.327
Thus, Steven, Paul, and Andrew together will finish the work in 11 1133/3467 days or 11.327 days Answer
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