Question:
If Gary can finish the work in 67 days and Christian can finish the same work in 72 days, then in how many days both can finish the work together?
Correct Answer
34 98/139 days or 34.705 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by Gary = 67 days
And, the number of days to finish the same work by Christian = 72 days
Thus, the number of days to finish the work by Gary and Christian together = ?
Here,
∵ In 67 days the work done by Gary = 1
∴ In 1 day, the work done by Gary = 1/67 part
Similarly,
∵ In 72 days the work done by Christian = 1
∴ In 1 day, the work done by Christian = 1/72 part
Now, in 1 day, the work done by Gary and Christian together
= In 1 day work done by Gary + In 1 day the work done by Christian
= 1/67 + 1/72
= 72 + 67/4824
= 139/4824 part of work
This means in 1 day, 139/4824 part of work is done by Gary and Christian working together.
Now, the number of days required to finish 139/4824 part of work by Gary + Christian working together = 1
∴ the number of days required to finish 1 work by Gary + Christian together
= 1/139/4824
= 1 × 4824/139 = 4824/139 days
= 34 98/139 days = or 34.705 days
Thus, Gary and Christian working together will finish the work in 34 98/139 days = or 34.705 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 Gary = 67 days
And the number of days required to finish the same work by Christian = 72 days
Thus, the number of days required to finish the work Gary and Christian working together = ?
Here a = 67 days
And, b = 72 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Gary and Christian working together
= 67 × 72/67 + 72 days
= 4824/139 days
= 34 98/139 days or 34.705
Thus, Gary and Christian together will finish the work in 34 98/139 days or 34.705 days Answer
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