Question:
If Linda can finish the work in 9 days and Charles can finish the same work in 13 days, then in how many days both can finish the work together?
Correct Answer
5 7/22 days or 5.318 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by Linda = 9 days
And, the number of days to finish the same work by Charles = 13 days
Thus, the number of days to finish the work by Linda and Charles together = ?
Here,
∵ In 9 days the work done by Linda = 1
∴ In 1 day, the work done by Linda = 1/9 part
Similarly,
∵ In 13 days the work done by Charles = 1
∴ In 1 day, the work done by Charles = 1/13 part
Now, in 1 day, the work done by Linda and Charles together
= In 1 day work done by Linda + In 1 day the work done by Charles
= 1/9 + 1/13
= 13 + 9/117
= 22/117 part of work
This means in 1 day, 22/117 part of work is done by Linda and Charles working together.
Now, the number of days required to finish 22/117 part of work by Linda + Charles working together = 1
∴ the number of days required to finish 1 work by Linda + Charles together
= 1/22/117
= 1 × 117/22 = 117/22 days
= 5 7/22 days = or 5.318 days
Thus, Linda and Charles working together will finish the work in 5 7/22 days = or 5.318 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 Linda = 9 days
And the number of days required to finish the same work by Charles = 13 days
Thus, the number of days required to finish the work Linda and Charles working together = ?
Here a = 9 days
And, b = 13 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Linda and Charles working together
= 9 × 13/9 + 13 days
= 117/22 days
= 5 7/22 days or 5.318
Thus, Linda and Charles together will finish the work in 5 7/22 days or 5.318 days Answer
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