Question:
If Gregory can finish the work in 89 days and Alan can finish the same work in 94 days, then in how many days both can finish the work together?
Correct Answer
45 131/183 days or 45.716 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by Gregory = 89 days
And, the number of days to finish the same work by Alan = 94 days
Thus, the number of days to finish the work by Gregory and Alan together = ?
Here,
∵ In 89 days the work done by Gregory = 1
∴ In 1 day, the work done by Gregory = 1/89 part
Similarly,
∵ In 94 days the work done by Alan = 1
∴ In 1 day, the work done by Alan = 1/94 part
Now, in 1 day, the work done by Gregory and Alan together
= In 1 day work done by Gregory + In 1 day the work done by Alan
= 1/89 + 1/94
= 94 + 89/8366
= 183/8366 part of work
This means in 1 day, 183/8366 part of work is done by Gregory and Alan working together.
Now, the number of days required to finish 183/8366 part of work by Gregory + Alan working together = 1
∴ the number of days required to finish 1 work by Gregory + Alan together
= 1/183/8366
= 1 × 8366/183 = 8366/183 days
= 45 131/183 days = or 45.716 days
Thus, Gregory and Alan working together will finish the work in 45 131/183 days = or 45.716 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 Gregory = 89 days
And the number of days required to finish the same work by Alan = 94 days
Thus, the number of days required to finish the work Gregory and Alan working together = ?
Here a = 89 days
And, b = 94 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Gregory and Alan working together
= 89 × 94/89 + 94 days
= 8366/183 days
= 45 131/183 days or 45.716
Thus, Gregory and Alan together will finish the work in 45 131/183 days or 45.716 days Answer
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