Question : If Robert can finish a work in 5 days and Bob can finish the same work in 6 days, then in how many days they both can finish the work working together?
Correct Answer 28/11 days
Solution & Explanation
Solution
Given,
The number of days to finish the work by Robert = 5 days
And, the number of days to finish the same work by Bob = 6 days
Thus, the number of days to finish the work by Rober and Bob working together = ?
Here, ∵ In 5 days the work done by Robert = 1
∴ In 1 day, the work done by Robert = 1/5
Similarly, ∵ In 6 days the work done by Bob = 1
∴ In 1 day, the work done by Bob = 1/6
Now, in 1 day, the work done by Robert and Bob working together
= In 1 day work done by Robert + In 1 day the work done by Bob
= 1/5 + 1/6
= 6 + 5/30
= 11/30
This means in 1 day, 11/30 part of work is done by Robert and Bob working together.
Now, the number of days required to finish 11/30 work by Robert + Bob working together = 1
∴ the number of days required to finish 1 work by Robert + Bob working together
= 1/11/30
= 1 × 30/11 days = 2 8/11 days
Thus, Robert and Bob working together will finish the work in 2 8/11 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 Robert = 5 days
And, the number of days to finish the same work by Bob = 6 days
Thus, the number of days to finish the work by Robert and Bob working together = ?
Here "a" = 5 days
And, "b" = 6 days
Thus, using formula a × b/a + b days
The number of days reqire to finish the work when Robert and Bob work together
= 5 × 6/5 + 6
= 30/11
= 2 8/11 days
Thus, Robert and Bob working together will finish the work in 2 8/11 days. Answer
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