Question:
If Linda can finish the work in 12 days and Charles can finish the same work in 17 days, then in how many days both can finish the work together?
Correct Answer
7 1/29 days or 7.034 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by Linda = 12 days
And, the number of days to finish the same work by Charles = 17 days
Thus, the number of days to finish the work by Linda and Charles together = ?
Here,
∵ In 12 days the work done by Linda = 1
∴ In 1 day, the work done by Linda = 1/12 part
Similarly,
∵ In 17 days the work done by Charles = 1
∴ In 1 day, the work done by Charles = 1/17 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
= 1/12 + 1/17
= 17 + 12/204
= 29/204 part of work
This means in 1 day, 29/204 part of work is done by Linda and Charles working together.
Now, the number of days required to finish 29/204 part of work by Linda + Charles working together = 1
∴ the number of days required to finish 1 work by Linda + Charles together
= 1/29/204
= 1 × 204/29 = 204/29 days
= 7 1/29 days = or 7.034 days
Thus, Linda and Charles working together will finish the work in 7 1/29 days = or 7.034 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 = 12 days
And the number of days required to finish the same work by Charles = 17 days
Thus, the number of days required to finish the work Linda and Charles working together = ?
Here a = 12 days
And, b = 17 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Linda and Charles working together
= 12 × 17/12 + 17 days
= 204/29 days
= 7 1/29 days or 7.034
Thus, Linda and Charles together will finish the work in 7 1/29 days or 7.034 days Answer
Similar Questions
(1) Nancy can finish a work in 24 days. Betty can finish the same work in 25 days while Margaret can finish the work in 26 days. How long will it take to finish it if they work together?
(2) If Christopher can finish the work in 22 days and Brian can finish the same work in 26 days, then in how many days both can finish the work together?
(3) William can finish a work in 15 days. Joseph can finish the same work in 20 days while Thomas can finish the work in 25 days. How long will it take to finish it if they work together?
(4) Michael can finish a work in 7 days. David can finish the same work in 8 days while William can finish the work in 9 days. How long will it take to finish it if they work together?
(5) Brian can finish a work in 49 days. Timothy can finish the same work in 54 days while Ronald can finish the work in 59 days. How long will it take to finish it if they work together?
(6) If Scott can finish the work in 81 days and Bryan can finish the same work in 86 days, then in how many days both can finish the work together?
(7) Daniel can finish a work in 23 days. Matthew can finish the same work in 24 days while Anthony can finish the work in 25 days. How long will it take to finish it if they work together?
(8) If Nancy can finish the work in 28 days and Ronald can finish the same work in 33 days, then in how many days both can finish the work together?
(9) If Jonathan can finish the work in 73 days and Sean can finish the same work in 78 days, then in how many days both can finish the work together?
(10) Lisa can finish a work in 22 days. Nancy can finish the same work in 23 days while Betty can finish the work in 24 days. How long will it take to finish it if they work together?