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 & 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
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