Question:
If Alexander can finish the work in 91 days and Wayne can finish the same work in 96 days, then in how many days both can finish the work together?
Correct Answer
46 134/187 days or 46.717 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by Alexander = 91 days
And, the number of days to finish the same work by Wayne = 96 days
Thus, the number of days to finish the work by Alexander and Wayne together = ?
Here,
∵ In 91 days the work done by Alexander = 1
∴ In 1 day, the work done by Alexander = 1/91 part
Similarly,
∵ In 96 days the work done by Wayne = 1
∴ In 1 day, the work done by Wayne = 1/96 part
Now, in 1 day, the work done by Alexander and Wayne together
= In 1 day work done by Alexander + In 1 day the work done by Wayne
= 1/91 + 1/96
= 96 + 91/8736
= 187/8736 part of work
This means in 1 day, 187/8736 part of work is done by Alexander and Wayne working together.
Now, the number of days required to finish 187/8736 part of work by Alexander + Wayne working together = 1
∴ the number of days required to finish 1 work by Alexander + Wayne together
= 1/187/8736
= 1 × 8736/187 = 8736/187 days
= 46 134/187 days = or 46.717 days
Thus, Alexander and Wayne working together will finish the work in 46 134/187 days = or 46.717 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 Alexander = 91 days
And the number of days required to finish the same work by Wayne = 96 days
Thus, the number of days required to finish the work Alexander and Wayne working together = ?
Here a = 91 days
And, b = 96 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Alexander and Wayne working together
= 91 × 96/91 + 96 days
= 8736/187 days
= 46 134/187 days or 46.717
Thus, Alexander and Wayne together will finish the work in 46 134/187 days or 46.717 days Answer
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