Question:
If Jonathan can finish the work in 73 days and Sean can finish the same work in 78 days, then in how many days both can finish the work together?
Correct Answer
37 107/151 days or 37.709 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by Jonathan = 73 days
And, the number of days to finish the same work by Sean = 78 days
Thus, the number of days to finish the work by Jonathan and Sean together = ?
Here,
∵ In 73 days the work done by Jonathan = 1
∴ In 1 day, the work done by Jonathan = 1/73 part
Similarly,
∵ In 78 days the work done by Sean = 1
∴ In 1 day, the work done by Sean = 1/78 part
Now, in 1 day, the work done by Jonathan and Sean together
= In 1 day work done by Jonathan + In 1 day the work done by Sean
= 1/73 + 1/78
= 78 + 73/5694
= 151/5694 part of work
This means in 1 day, 151/5694 part of work is done by Jonathan and Sean working together.
Now, the number of days required to finish 151/5694 part of work by Jonathan + Sean working together = 1
∴ the number of days required to finish 1 work by Jonathan + Sean together
= 1/151/5694
= 1 × 5694/151 = 5694/151 days
= 37 107/151 days = or 37.709 days
Thus, Jonathan and Sean working together will finish the work in 37 107/151 days = or 37.709 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 Jonathan = 73 days
And the number of days required to finish the same work by Sean = 78 days
Thus, the number of days required to finish the work Jonathan and Sean working together = ?
Here a = 73 days
And, b = 78 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Jonathan and Sean working together
= 73 × 78/73 + 78 days
= 5694/151 days
= 37 107/151 days or 37.709
Thus, Jonathan and Sean together will finish the work in 37 107/151 days or 37.709 days Answer
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