Question:
If Mary can finish the work in 25 days and Michael can finish the same work in 41 days, then in how many days both can finish the work together?
Correct Answer
15 35/66 days or 15.53 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by Mary = 25 days
And, the number of days to finish the same work by Michael = 41 days
Thus, the number of days to finish the work by Mary and Michael together = ?
Here,
∵ In 25 days the work done by Mary = 1
∴ In 1 day, the work done by Mary = 1/25 part
Similarly,
∵ In 41 days the work done by Michael = 1
∴ In 1 day, the work done by Michael = 1/41 part
Now, in 1 day, the work done by Mary and Michael together
= In 1 day work done by Mary + In 1 day the work done by Michael
= 1/25 + 1/41
= 41 + 25/1025
= 66/1025 part of work
This means in 1 day, 66/1025 part of work is done by Mary and Michael working together.
Now, the number of days required to finish 66/1025 part of work by Mary + Michael working together = 1
∴ the number of days required to finish 1 work by Mary + Michael together
= 1/66/1025
= 1 × 1025/66 = 1025/66 days
= 15 35/66 days = or 15.53 days
Thus, Mary and Michael working together will finish the work in 15 35/66 days = or 15.53 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 Mary = 25 days
And the number of days required to finish the same work by Michael = 41 days
Thus, the number of days required to finish the work Mary and Michael working together = ?
Here a = 25 days
And, b = 41 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Mary and Michael working together
= 25 × 41/25 + 41 days
= 1025/66 days
= 15 35/66 days or 15.53
Thus, Mary and Michael together will finish the work in 15 35/66 days or 15.53 days Answer
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