Question:
If Margaret can finish the work in 29 days and Ryan can finish the same work in 32 days, then in how many days both can finish the work together?
Correct Answer
15 13/61 days or 15.213 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by Margaret = 29 days
And, the number of days to finish the same work by Ryan = 32 days
Thus, the number of days to finish the work by Margaret and Ryan together = ?
Here,
∵ In 29 days the work done by Margaret = 1
∴ In 1 day, the work done by Margaret = 1/29 part
Similarly,
∵ In 32 days the work done by Ryan = 1
∴ In 1 day, the work done by Ryan = 1/32 part
Now, in 1 day, the work done by Margaret and Ryan together
= In 1 day work done by Margaret + In 1 day the work done by Ryan
= 1/29 + 1/32
= 32 + 29/928
= 61/928 part of work
This means in 1 day, 61/928 part of work is done by Margaret and Ryan working together.
Now, the number of days required to finish 61/928 part of work by Margaret + Ryan working together = 1
∴ the number of days required to finish 1 work by Margaret + Ryan together
= 1/61/928
= 1 × 928/61 = 928/61 days
= 15 13/61 days = or 15.213 days
Thus, Margaret and Ryan working together will finish the work in 15 13/61 days = or 15.213 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 Margaret = 29 days
And the number of days required to finish the same work by Ryan = 32 days
Thus, the number of days required to finish the work Margaret and Ryan working together = ?
Here a = 29 days
And, b = 32 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Margaret and Ryan working together
= 29 × 32/29 + 32 days
= 928/61 days
= 15 13/61 days or 15.213
Thus, Margaret and Ryan together will finish the work in 15 13/61 days or 15.213 days Answer
Similar Questions
(1) 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?
(2) Nancy can finish a work in 28 days. Margaret can finish the same work in 33 days while Sandra can finish the work in 38 days. How long will it take to finish it if they work together?
(3) Carol can finish a work in 42 days. Amanda can finish the same work in 43 days while Dorothy can finish the work in 44 days. How long will it take to finish it if they work together?
(4) If Jennifer can finish the work in 29 days and Joseph can finish the same work in 45 days, then in how many days both can finish the work together?
(5) If William can finish the work in 12 days and Matthew can finish the same work in 15 days, then in how many days both can finish the work together?
(6) Christopher can finish a work in 25 days. Matthew can finish the same work in 30 days while Anthony can finish the work in 35 days. How long will it take to finish it if they work together?
(7) If Joshua can finish the work in 43 days and Benjamin can finish the same work in 48 days, then in how many days both can finish the work together?
(8) 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?
(9) John can finish a work in 9 days. David can finish the same work in 14 days while William can finish the work in 19 days. How long will it take to finish it if they work together?
(10) Linda can finish a work in 12 days. Barbara can finish the same work in 17 days while Susan can finish the work in 22 days. How long will it take to finish it if they work together?