Question:
If Mary can finish the work in 6 days and Michael can finish the same work in 11 days, then in how many days both can finish the work together?
Correct Answer
3 15/17 days or 3.882 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by Mary = 6 days
And, the number of days to finish the same work by Michael = 11 days
Thus, the number of days to finish the work by Mary and Michael together = ?
Here,
∵ In 6 days the work done by Mary = 1
∴ In 1 day, the work done by Mary = 1/6 part
Similarly,
∵ In 11 days the work done by Michael = 1
∴ In 1 day, the work done by Michael = 1/11 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
= 1/6 + 1/11
= 11 + 6/66
= 17/66 part of work
This means in 1 day, 17/66 part of work is done by Mary and Michael working together.
Now, the number of days required to finish 17/66 part of work by Mary + Michael working together = 1
∴ the number of days required to finish 1 work by Mary + Michael together
= 1/17/66
= 1 × 66/17 = 66/17 days
= 3 15/17 days = or 3.882 days
Thus, Mary and Michael working together will finish the work in 3 15/17 days = or 3.882 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 = 6 days
And the number of days required to finish the same work by Michael = 11 days
Thus, the number of days required to finish the work Mary and Michael working together = ?
Here a = 6 days
And, b = 11 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Mary and Michael working together
= 6 × 11/6 + 11 days
= 66/17 days
= 3 15/17 days or 3.882
Thus, Mary and Michael together will finish the work in 3 15/17 days or 3.882 days Answer
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