Question:
If Annie can finish a work in 5 days and Bobby can finish the same work in 10 days, then in how many days they both can finish the work working together?
Correct Answer
31/3 days or 3.33 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by Annie = 5 days
And, the number of days to finish the same work by Bobby = 10 days
Thus, the number of days to finish the work by Annie and Bobby working together = ?
Here, ∵ In 5 days the work done by Annie = 1
∴ In 1 day, the work done by Annie = 1/5
Similarly, ∵ In 10 days the work done by Bobby = 1
∴ In 1 day, the work done by Bobby = 1/10
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
= 1/5 + 1/10
= 2 + 1/10
= 3/10
This means in 1 day, 3/10 part of work is done by Annie and Bobby working together.
Now, the number of days required to finish 3/10 work by Annie + Bobby working together = 1
∴ the number of days required to finish 1 work by Annie + Bobby working together
= 1/3/10
= 1 × 10/3 days = 3 1/3 days
Thus, Annie and Bobby working together will finish the work in 3 1/3 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 = 5 days
And, the number of days to finish the same work by Bobby = 10 days
Thus, the number of days to finish the work by Annie and Bobby working together = ?
Here "a" = 5 days
And, "b" = 10 days
Thus, using formula a × b/a + b days
The number of days require to finish the work when Annie and Bobby working together
= 5 × 10/5 + 10
= 50 10/15 3
= 10/3 days
= 3 1/3 days or 3.33 days
Thus, Annie and Bobby working together will finish the work in 3 1/3 days or 3.33 days Answer
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