Question : If Paul can finish the work in 39 days and Larry can finish the same work in 44 days, then in how many days both can finish the work together?
Correct Answer 20 56/83 days or 20.675 days
Solution & Explanation
Solution
Given,
The number of days to finish the work by Paul = 39 days
And, the number of days to finish the same work by Larry = 44 days
Thus, the number of days to finish the work by Paul and Larry together = ?
Here,
∵ In 39 days the work done by Paul = 1
∴ In 1 day, the work done by Paul = 1/39 part
Similarly,
∵ In 44 days the work done by Larry = 1
∴ In 1 day, the work done by Larry = 1/44 part
Now, in 1 day, the work done by Paul and Larry together
= In 1 day work done by Paul + In 1 day the work done by Larry
= 1/39 + 1/44
= 44 + 39/1716
= 83/1716 part of work
This means in 1 day, 83/1716 part of work is done by Paul and Larry working together.
Now, the number of days required to finish 83/1716 part of work by Paul + Larry working together = 1
∴ the number of days required to finish 1 work by Paul + Larry together
= 1/83/1716
= 1 × 1716/83 = 1716/83 days
= 20 56/83 days = or 20.675 days
Thus, Paul and Larry working together will finish the work in 20 56/83 days = or 20.675 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, and B can finish the same work in b days,
then working together the number of days require to finish the work
= a × b/a + b days.
Here given,
The number of days required to finish the work by Paul = 39 days
And the number of days required to finish the same work by Larry = 44 days
Thus, the number of days required to finish the work Paul and Larry working together = ?
Here a = 39 days
And, b = 44 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Paul and Larry working together
= 39 × 44/39 + 44 days
= 1716/83 days
= 20 56/83 days or 20.675
Thus, Paul and Larry together will finish the work in 20 56/83 days or 20.675 days Answer
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