Question:
If Brian can finish the work in 49 days and Raymond can finish the same work in 54 days, then in how many days both can finish the work together?
Correct Answer
25 71/103 days or 25.689 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by Brian = 49 days
And, the number of days to finish the same work by Raymond = 54 days
Thus, the number of days to finish the work by Brian and Raymond together = ?
Here,
∵ In 49 days the work done by Brian = 1
∴ In 1 day, the work done by Brian = 1/49 part
Similarly,
∵ In 54 days the work done by Raymond = 1
∴ In 1 day, the work done by Raymond = 1/54 part
Now, in 1 day, the work done by Brian and Raymond together
= In 1 day work done by Brian + In 1 day the work done by Raymond
= 1/49 + 1/54
= 54 + 49/2646
= 103/2646 part of work
This means in 1 day, 103/2646 part of work is done by Brian and Raymond working together.
Now, the number of days required to finish 103/2646 part of work by Brian + Raymond working together = 1
∴ the number of days required to finish 1 work by Brian + Raymond together
= 1/103/2646
= 1 × 2646/103 = 2646/103 days
= 25 71/103 days = or 25.689 days
Thus, Brian and Raymond working together will finish the work in 25 71/103 days = or 25.689 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 Brian = 49 days
And the number of days required to finish the same work by Raymond = 54 days
Thus, the number of days required to finish the work Brian and Raymond working together = ?
Here a = 49 days
And, b = 54 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Brian and Raymond working together
= 49 × 54/49 + 54 days
= 2646/103 days
= 25 71/103 days or 25.689
Thus, Brian and Raymond together will finish the work in 25 71/103 days or 25.689 days Answer
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