Question:
If Raymond can finish the work in 97 days and Eugene can finish the same work in 102 days, then in how many days both can finish the work together?
Correct Answer
49 143/199 days or 49.719 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by Raymond = 97 days
And, the number of days to finish the same work by Eugene = 102 days
Thus, the number of days to finish the work by Raymond and Eugene together = ?
Here,
∵ In 97 days the work done by Raymond = 1
∴ In 1 day, the work done by Raymond = 1/97 part
Similarly,
∵ In 102 days the work done by Eugene = 1
∴ In 1 day, the work done by Eugene = 1/102 part
Now, in 1 day, the work done by Raymond and Eugene together
= In 1 day work done by Raymond + In 1 day the work done by Eugene
= 1/97 + 1/102
= 102 + 97/9894
= 199/9894 part of work
This means in 1 day, 199/9894 part of work is done by Raymond and Eugene working together.
Now, the number of days required to finish 199/9894 part of work by Raymond + Eugene working together = 1
∴ the number of days required to finish 1 work by Raymond + Eugene together
= 1/199/9894
= 1 × 9894/199 = 9894/199 days
= 49 143/199 days = or 49.719 days
Thus, Raymond and Eugene working together will finish the work in 49 143/199 days = or 49.719 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 Raymond = 97 days
And the number of days required to finish the same work by Eugene = 102 days
Thus, the number of days required to finish the work Raymond and Eugene working together = ?
Here a = 97 days
And, b = 102 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Raymond and Eugene working together
= 97 × 102/97 + 102 days
= 9894/199 days
= 49 143/199 days or 49.719
Thus, Raymond and Eugene together will finish the work in 49 143/199 days or 49.719 days Answer
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