Question:
If Lisa can finish the work in 23 days and George can finish the same work in 26 days, then in how many days both can finish the work together?
Correct Answer
12 10/49 days or 12.204 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by Lisa = 23 days
And, the number of days to finish the same work by George = 26 days
Thus, the number of days to finish the work by Lisa and George together = ?
Here,
∵ In 23 days the work done by Lisa = 1
∴ In 1 day, the work done by Lisa = 1/23 part
Similarly,
∵ In 26 days the work done by George = 1
∴ In 1 day, the work done by George = 1/26 part
Now, in 1 day, the work done by Lisa and George together
= In 1 day work done by Lisa + In 1 day the work done by George
= 1/23 + 1/26
= 26 + 23/598
= 49/598 part of work
This means in 1 day, 49/598 part of work is done by Lisa and George working together.
Now, the number of days required to finish 49/598 part of work by Lisa + George working together = 1
∴ the number of days required to finish 1 work by Lisa + George together
= 1/49/598
= 1 × 598/49 = 598/49 days
= 12 10/49 days = or 12.204 days
Thus, Lisa and George working together will finish the work in 12 10/49 days = or 12.204 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 Lisa = 23 days
And the number of days required to finish the same work by George = 26 days
Thus, the number of days required to finish the work Lisa and George working together = ?
Here a = 23 days
And, b = 26 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Lisa and George working together
= 23 × 26/23 + 26 days
= 598/49 days
= 12 10/49 days or 12.204
Thus, Lisa and George together will finish the work in 12 10/49 days or 12.204 days Answer
Similar Questions
(1) If Charles can finish the work in 20 days and Kenneth can finish the same work in 24 days, then in how many days both can finish the work together?
(2) Lisa can finish a work in 26 days. Betty can finish the same work in 31 days while Margaret can finish the work in 36 days. How long will it take to finish it if they work together?
(3) Brenda can finish a work in 76 days. Emma can finish the same work in 81 days while Nicole can finish the work in 86 days. How long will it take to finish it if they work together?
(4) Anna can finish a work in 74 days. Pamela can finish the same work in 79 days while Emma can finish the work in 84 days. How long will it take to finish it if they work together?
(5) If Emily can finish the work in 37 days and Justin can finish the same work in 41 days, then in how many days both can finish the work together?
(6) 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?
(7) If John can finish the work in 6 days and Richard can finish the same work in 10 days, then in how many days both can finish the work together?
(8) If Sandra can finish the work in 31 days and Gary can finish the same work in 35 days, then in how many days both can finish the work together?
(9) Daniel can finish a work in 27 days. Anthony can finish the same work in 32 days while Mark can finish the work in 37 days. How long will it take to finish it if they work together?
(10) If Jack can finish the work in 99 days and Bobby can finish the same work in 104 days, then in how many days both can finish the work together?