Question:
If Rachel can finish the work in 94 days and Roy can finish the same work in 99 days, then in how many days both can finish the work together?
Correct Answer
48 42/193 days or 48.218 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by Rachel = 94 days
And, the number of days to finish the same work by Roy = 99 days
Thus, the number of days to finish the work by Rachel and Roy together = ?
Here,
∵ In 94 days the work done by Rachel = 1
∴ In 1 day, the work done by Rachel = 1/94 part
Similarly,
∵ In 99 days the work done by Roy = 1
∴ In 1 day, the work done by Roy = 1/99 part
Now, in 1 day, the work done by Rachel and Roy together
= In 1 day work done by Rachel + In 1 day the work done by Roy
= 1/94 + 1/99
= 99 + 94/9306
= 193/9306 part of work
This means in 1 day, 193/9306 part of work is done by Rachel and Roy working together.
Now, the number of days required to finish 193/9306 part of work by Rachel + Roy working together = 1
∴ the number of days required to finish 1 work by Rachel + Roy together
= 1/193/9306
= 1 × 9306/193 = 9306/193 days
= 48 42/193 days = or 48.218 days
Thus, Rachel and Roy working together will finish the work in 48 42/193 days = or 48.218 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 Rachel = 94 days
And the number of days required to finish the same work by Roy = 99 days
Thus, the number of days required to finish the work Rachel and Roy working together = ?
Here a = 94 days
And, b = 99 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Rachel and Roy working together
= 94 × 99/94 + 99 days
= 9306/193 days
= 48 42/193 days or 48.218
Thus, Rachel and Roy together will finish the work in 48 42/193 days or 48.218 days Answer
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