Question:
If Thomas can finish the work in 18 days and Andrew can finish the same work in 21 days, then in how many days both can finish the work together?
Correct Answer
9 9/13 days or 9.692 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by Thomas = 18 days
And, the number of days to finish the same work by Andrew = 21 days
Thus, the number of days to finish the work by Thomas and Andrew together = ?
Here,
∵ In 18 days the work done by Thomas = 1
∴ In 1 day, the work done by Thomas = 1/18 part
Similarly,
∵ In 21 days the work done by Andrew = 1
∴ In 1 day, the work done by Andrew = 1/21 part
Now, in 1 day, the work done by Thomas and Andrew together
= In 1 day work done by Thomas + In 1 day the work done by Andrew
= 1/18 + 1/21
= 7 + 6/126
= 13/126 part of work
This means in 1 day, 13/126 part of work is done by Thomas and Andrew working together.
Now, the number of days required to finish 13/126 part of work by Thomas + Andrew working together = 1
∴ the number of days required to finish 1 work by Thomas + Andrew together
= 1/13/126
= 1 × 126/13 = 126/13 days
= 9 9/13 days = or 9.692 days
Thus, Thomas and Andrew working together will finish the work in 9 9/13 days = or 9.692 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 Thomas = 18 days
And the number of days required to finish the same work by Andrew = 21 days
Thus, the number of days required to finish the work Thomas and Andrew working together = ?
Here a = 18 days
And, b = 21 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Thomas and Andrew working together
= 18 × 21/18 + 21 days
= 378/39 days
= 378 ÷ 3/39 ÷ 3 = 126/13 days
= 9 9/13 days or 9.692
Thus, Thomas and Andrew together will finish the work in 9 9/13 days or 9.692 days Answer
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