Question:
If Michael can finish the work in 8 days and Thomas can finish the same work in 11 days, then in how many days both can finish the work together?
Correct Answer
4 12/19 days or 4.632 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by Michael = 8 days
And, the number of days to finish the same work by Thomas = 11 days
Thus, the number of days to finish the work by Michael and Thomas together = ?
Here,
∵ In 8 days the work done by Michael = 1
∴ In 1 day, the work done by Michael = 1/8 part
Similarly,
∵ In 11 days the work done by Thomas = 1
∴ In 1 day, the work done by Thomas = 1/11 part
Now, in 1 day, the work done by Michael and Thomas together
= In 1 day work done by Michael + In 1 day the work done by Thomas
= 1/8 + 1/11
= 11 + 8/88
= 19/88 part of work
This means in 1 day, 19/88 part of work is done by Michael and Thomas working together.
Now, the number of days required to finish 19/88 part of work by Michael + Thomas working together = 1
∴ the number of days required to finish 1 work by Michael + Thomas together
= 1/19/88
= 1 × 88/19 = 88/19 days
= 4 12/19 days = or 4.632 days
Thus, Michael and Thomas working together will finish the work in 4 12/19 days = or 4.632 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 Michael = 8 days
And the number of days required to finish the same work by Thomas = 11 days
Thus, the number of days required to finish the work Michael and Thomas working together = ?
Here a = 8 days
And, b = 11 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Michael and Thomas working together
= 8 × 11/8 + 11 days
= 88/19 days
= 4 12/19 days or 4.632
Thus, Michael and Thomas together will finish the work in 4 12/19 days or 4.632 days Answer
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