Question : If Mary can finish the work in 3 days and Michael can finish the same work in 7 days, then in how many days both can finish the work together?
Correct Answer 2 1/10 days or 2.1 days
Solution & Explanation
Solution
Given,
The number of days to finish the work by Mary = 3 days
And, the number of days to finish the same work by Michael = 7 days
Thus, the number of days to finish the work by Mary and Michael together = ?
Here,
∵ In 3 days the work done by Mary = 1
∴ In 1 day, the work done by Mary = 1/3 part
Similarly,
∵ In 7 days the work done by Michael = 1
∴ In 1 day, the work done by Michael = 1/7 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
= 1/3 + 1/7
= 7 + 3/21
= 10/21 part of work
This means in 1 day, 10/21 part of work is done by Mary and Michael working together.
Now, the number of days required to finish 10/21 part of work by Mary + Michael working together = 1
∴ the number of days required to finish 1 work by Mary + Michael together
= 1/10/21
= 1 × 21/10 = 21/10 days
= 2 1/10 days = or 2.1 days
Thus, Mary and Michael working together will finish the work in 2 1/10 days = or 2.1 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 = 3 days
And the number of days required to finish the same work by Michael = 7 days
Thus, the number of days required to finish the work Mary and Michael working together = ?
Here a = 3 days
And, b = 7 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Mary and Michael working together
= 3 × 7/3 + 7 days
= 21/10 days
= 2 1/10 days or 2.1
Thus, Mary and Michael together will finish the work in 2 1/10 days or 2.1 days Answer
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