Question:
If Annie can finish a work in 2 days and Bobby can finish the same work in 3 days, then in how many days they both can finish the work working together?
Correct Answer
6/5 days or 11/5 days or 1.2 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by Annie = 2 days
And, the number of days to finish the same work by Bobby = 3 days
Thus, the number of days to finish the work by Annie and Bobby working together = ?
Here, ∵ In 2 days the work done by Annie = 1
∴ In 1 day, the work done by Annie = 1/2 part
Similarly, ∵ In 3 days the work done by Bobby = 1
∴ In 1 day, the work done by Bobby = 1/3 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
= 1/2 + 1/3
= 3 + 2/6
= 5/6
This means in 1 day, 5/6 part of work is done by Annie and Bobby working together.
Now, the number of days required to finish 5/6 part work by Annie + Bobby working together = 1
∴ the number of days required to finish 1 work by Robert + Bob working together
= 1/5/6
= 1 × 6/5 days = 6/5 days
= 6/5 or 1 1/5 days or 1.2 days
Thus, Annie and Bobby working together will finish the work in 6/5 or 1 1/5 days or 1.2 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 = 2 days
And, the number of days to finish the same work by Bobby = 3 days
Thus, the number of days to finish the work by Annie and Bobby working together = ?
Here "a" = 2 days
And, "b" = 3 days
Thus, using formula a × b/a + b days
The number of days require to finish the work when Annie and Bobby working together
= 2 × 3/2 + 3
= 6/5 days or 11/5 days or 1.2 days
Thus, Annie and Bobby working together will finish the work in 6/5 days or 11/5 days or 1.2 days Answer
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