Question:
If Annie can finish a work in 6 days and Bobby can finish the same work in 12 days, then in how many days they both can finish the work working together?
Correct Answer
4 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by Annie = 6 days
And, the number of days to finish the same work by Bobby = 12 days
Thus, the number of days to finish the work by Annie and Bobby working together = ?
Here, ∵ In 6 days the work done by Annie = 1
∴ In 1 day, the work done by Annie = 1/6 part
Similarly, ∵ In 12 days the work done by Bobby = 1
∴ In 1 day, the work done by Bobby = 1/12 part
Now, in 1 day, the work done by Annie and Bobby working together
= In 1 day work done by Annie + In 1 day the work done by Bobby
= 1/6 + 1/12
= 2 + 1/12
= 3 1/12 4 = 1/4 part of work
This means in 1 day, 1/4 part of work is done by Annie and Bobby working together.
Now, the number of days required to finish 1/4 part work by Annie + Bobby working together = 1
∴ the number of days required to finish 1 work by Robert + Bob working together
= 1/1/4
= 1 × 4/1 days = 4 days
Thus, Annie and Bobby working together will finish the work in 4 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 to finish the work by Annie =6 days
And, the number of days to finish the same work by Bobby = 12 days
Thus, the number of days to finish the work by Annie and Bobby working together = ?
Here "a" = 6 days
And, "b" = 12 days
Thus, using formula a × b/a + b days
The number of days require to finish the work when Annie and Bobby working together
= 6 × 12/6 + 12
= 72 4/18 = 4 days
Thus, Annie and Bobby working together will finish the work in 4 days Answer
Similar Questions
(1) Samuel can finish a work in 87 days. Alexander can finish the same work in 92 days while Frank can finish the work in 97 days. How long will it take to finish it if they work together?
(2) If Robert can finish the work in 26 days and David can finish the same work in 42 days, then in how many days both can finish the work together?
(3) If Robert can finish a work in 4 days and Bob can finish the same work in 6 days, then in how many days they both can finish the work working together?
(4) If David can finish the work in 32 days and Christopher can finish the same work in 48 days, then in how many days both can finish the work together?
(5) If David can finish the work in 13 days and Christopher can finish the same work in 18 days, then in how many days both can finish the work together?
(6) Karen can finish a work in 20 days. Lisa can finish the same work in 21 days while Nancy can finish the work in 22 days. How long will it take to finish it if they work together?
(7) Matthew can finish a work in 29 days. Mark can finish the same work in 34 days while Donald can finish the work in 39 days. How long will it take to finish it if they work together?
(8) Richard can finish a work in 17 days. Thomas can finish the same work in 22 days while Charles can finish the work in 27 days. How long will it take to finish it if they work together?
(9) If Mark can finish the work in 30 days and Jacob can finish the same work in 34 days, then in how many days both can finish the work together?
(10) Helen can finish a work in 84 days. Katherine can finish the same work in 89 days while Christine can finish the work in 94 days. How long will it take to finish it if they work together?