Question : If Jack can finish the work in 20 days and Bill can finish the same work in 30 days, then in how many days they both can finish the work working together?
Correct Answer 12 days
Solution & Explanation
Solution
Given,
The number of days to finish the work by Jack = 20 days
And, the number of days to finish the same work by Bill = 30 days
Thus, the number of days to finish the work by Jack and Bill working together = ?
Here, ∵ In 20 days the work done by Jack = 1
∴ In 1 day, the work done by Jack = 1/20 part
Similarly, ∵ In 30 days the work done by Bill = 1
∴ In 1 day, the work done by Bill = 1/30 part
Now, in 1 day, the work done by Jack and Bill working together
= In 1 day work done by Jack + In 1 day the work done by Bill
= 1/20 + 1/30
= 3 + 2/60
= 5 1/60 12 = 1/12 part of work
This means in 1 day, 1/12 part of work is done by Jack and Bill working together.
Now, the number of days required to finish 1/12 parts of work by Jack + Bill working together = 1
∴ the number of days required to finish 1 work by Robert + Bob working together
= 1/1/12
= 1 × 12/1 days = 12 days
Thus, Jack and Bill working together will finish the work in 12 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 to finish the work by Jack = 20 days
And, the number of days to finish the same work by Bill = 30 days
Thus, the number of days to finish the work by Jack and Bill working together = ?
Here "a" = 20 days
And, "b" = 30 days
Thus, using formula a × b/a + b days
The number of days require to finish the work when Jack and Bill working together
= 20 × 30/20 + 30
= 600 12/50 = 12 days
Thus, Jack and Bill working together will finish the work in 12 days Answer
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