Question:
If Linda can finish the work in 9 days and Charles can finish the same work in 12 days, then in how many days both can finish the work together?
Correct Answer
5 1/7 days or 5.143 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 = 12 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 12 days the work done by Charles = 1
∴ In 1 day, the work done by Charles = 1/12 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 + 1/12
= 4 + 3/36
= 7/36 part of work
This means in 1 day, 7/36 part of work is done by Linda and Charles working together.
Now, the number of days required to finish 7/36 part of work by Linda + Charles working together = 1
∴ the number of days required to finish 1 work by Linda + Charles together
= 1/7/36
= 1 × 36/7 = 36/7 days
= 5 1/7 days = or 5.143 days
Thus, Linda and Charles working together will finish the work in 5 1/7 days = or 5.143 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 = 12 days
Thus, the number of days required to finish the work Linda and Charles working together = ?
Here a = 9 days
And, b = 12 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 × 12/9 + 12 days
= 108/21 days
= 108 ÷ 3/21 ÷ 3 = 36/7 days
= 5 1/7 days or 5.143
Thus, Linda and Charles together will finish the work in 5 1/7 days or 5.143 days Answer
Similar Questions
(1) Steven can finish a work in 37 days. Andrew can finish the same work in 42 days while Joshua can finish the work in 47 days. How long will it take to finish it if they work together?
(2) If Michael can finish the work in 30 days and Thomas can finish the same work in 46 days, then in how many days both can finish the work together?
(3) If Kathleen can finish the work in 66 days and Jeremy can finish the same work in 71 days, then in how many days both can finish the work together?
(4) If Richard can finish the work in 14 days and Mark can finish the same work in 18 days, then in how many days both can finish the work together?
(5) If Michelle can finish the work in 44 days and Samuel can finish the same work in 49 days, then in how many days both can finish the work together?
(6) 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?
(7) Nicole can finish a work in 82 days. Samantha can finish the same work in 87 days while Katherine can finish the work in 92 days. How long will it take to finish it if they work together?
(8) Rebecca can finish a work in 58 days. Laura can finish the same work in 63 days while Cynthia can finish the work in 68 days. How long will it take to finish it if they work together?
(9) If Paul can finish the work in 36 days and Larry can finish the same work in 39 days, then in how many days both can finish the work together?
(10) Melissa can finish a work in 52 days. Stephanie can finish the same work in 57 days while Rebecca can finish the work in 62 days. How long will it take to finish it if they work together?