Question : If Jack can finish a work in 8 days and Bill can finish the same work in 12 days, then in how many days they both can finish the work working together?
Correct Answer 4 4/5 days or 4.8 days
Solution & Explanation
Solution
Given,
The number of days to finish the work by Jack = 8 days
And, the number of days to finish the same work by Bill = 12 days
Thus, the number of days to finish the work by Jack and Bill working together = ?
Here, ∵ In 8 days the work done by Jack = 1
∴ In 1 day, the work done by Jack = 1/8 part
Similarly, ∵ In 12 days the work done by Bill = 1
∴ In 1 day, the work done by Bill = 1/12 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
= 1/8 + 1/12
= 3 + 2/24
= 5/24 part of work
This means in 1 day, 5/24 part of work is done by Jack and Bill working together.
Now, the number of days required to finish 5/24 part of work by Jack + Bill working together = 1
∴ the number of days required to finish 1 work by Robert + Bob working together
= 1/5/24
= 1 × 24/5 days = 24/5 days
= 4 4/5 days = 4.8 days
Thus, Jack and Bill working together will finish the work in 4 4/5 days = 4.8 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 = 8 days
And, the number of days to finish the same work by Bill = 12 days
Thus, the number of days to finish the work by Jack and Bill working together = ?
Here "a" = 8 days
And, "b" = 12 days
Thus, using formula a × b/a + b days
The number of days require to finish the work when Jack and Bill working together
= 8 × 12/8 + 12
= 24 × 4/5 × 4 = 24/5 days
= 4 4/5 days or 4.8 days
Thus, Jack and Bill working together will finish the work in 4 4/5 days or 4.8 days Answer
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