Question:
If Joshua can finish the work in 40 days and Benjamin can finish the same work in 43 days, then in how many days both can finish the work together?
Correct Answer
20 60/83 days or 20.723 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by Joshua = 40 days
And, the number of days to finish the same work by Benjamin = 43 days
Thus, the number of days to finish the work by Joshua and Benjamin together = ?
Here,
∵ In 40 days the work done by Joshua = 1
∴ In 1 day, the work done by Joshua = 1/40 part
Similarly,
∵ In 43 days the work done by Benjamin = 1
∴ In 1 day, the work done by Benjamin = 1/43 part
Now, in 1 day, the work done by Joshua and Benjamin together
= In 1 day work done by Joshua + In 1 day the work done by Benjamin
= 1/40 + 1/43
= 43 + 40/1720
= 83/1720 part of work
This means in 1 day, 83/1720 part of work is done by Joshua and Benjamin working together.
Now, the number of days required to finish 83/1720 part of work by Joshua + Benjamin working together = 1
∴ the number of days required to finish 1 work by Joshua + Benjamin together
= 1/83/1720
= 1 × 1720/83 = 1720/83 days
= 20 60/83 days = or 20.723 days
Thus, Joshua and Benjamin working together will finish the work in 20 60/83 days = or 20.723 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 Joshua = 40 days
And the number of days required to finish the same work by Benjamin = 43 days
Thus, the number of days required to finish the work Joshua and Benjamin working together = ?
Here a = 40 days
And, b = 43 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Joshua and Benjamin working together
= 40 × 43/40 + 43 days
= 1720/83 days
= 20 60/83 days or 20.723
Thus, Joshua and Benjamin together will finish the work in 20 60/83 days or 20.723 days Answer
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