Question:
If Nancy can finish the work in 25 days and Ronald can finish the same work in 29 days, then in how many days both can finish the work together?
Correct Answer
13 23/54 days or 13.426 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by Nancy = 25 days
And, the number of days to finish the same work by Ronald = 29 days
Thus, the number of days to finish the work by Nancy and Ronald together = ?
Here,
∵ In 25 days the work done by Nancy = 1
∴ In 1 day, the work done by Nancy = 1/25 part
Similarly,
∵ In 29 days the work done by Ronald = 1
∴ In 1 day, the work done by Ronald = 1/29 part
Now, in 1 day, the work done by Nancy and Ronald together
= In 1 day work done by Nancy + In 1 day the work done by Ronald
= 1/25 + 1/29
= 29 + 25/725
= 54/725 part of work
This means in 1 day, 54/725 part of work is done by Nancy and Ronald working together.
Now, the number of days required to finish 54/725 part of work by Nancy + Ronald working together = 1
∴ the number of days required to finish 1 work by Nancy + Ronald together
= 1/54/725
= 1 × 725/54 = 725/54 days
= 13 23/54 days = or 13.426 days
Thus, Nancy and Ronald working together will finish the work in 13 23/54 days = or 13.426 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 required to finish the work by Nancy = 25 days
And the number of days required to finish the same work by Ronald = 29 days
Thus, the number of days required to finish the work Nancy and Ronald working together = ?
Here a = 25 days
And, b = 29 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Nancy and Ronald working together
= 25 × 29/25 + 29 days
= 725/54 days
= 13 23/54 days or 13.426
Thus, Nancy and Ronald together will finish the work in 13 23/54 days or 13.426 days Answer
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