Question:
If Frank can finish the work in 93 days and Randy can finish the same work in 98 days, then in how many days both can finish the work together?
Correct Answer
47 137/191 days or 47.717 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by Frank = 93 days
And, the number of days to finish the same work by Randy = 98 days
Thus, the number of days to finish the work by Frank and Randy together = ?
Here,
∵ In 93 days the work done by Frank = 1
∴ In 1 day, the work done by Frank = 1/93 part
Similarly,
∵ In 98 days the work done by Randy = 1
∴ In 1 day, the work done by Randy = 1/98 part
Now, in 1 day, the work done by Frank and Randy together
= In 1 day work done by Frank + In 1 day the work done by Randy
= 1/93 + 1/98
= 98 + 93/9114
= 191/9114 part of work
This means in 1 day, 191/9114 part of work is done by Frank and Randy working together.
Now, the number of days required to finish 191/9114 part of work by Frank + Randy working together = 1
∴ the number of days required to finish 1 work by Frank + Randy together
= 1/191/9114
= 1 × 9114/191 = 9114/191 days
= 47 137/191 days = or 47.717 days
Thus, Frank and Randy working together will finish the work in 47 137/191 days = or 47.717 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 Frank = 93 days
And the number of days required to finish the same work by Randy = 98 days
Thus, the number of days required to finish the work Frank and Randy working together = ?
Here a = 93 days
And, b = 98 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Frank and Randy working together
= 93 × 98/93 + 98 days
= 9114/191 days
= 47 137/191 days or 47.717
Thus, Frank and Randy together will finish the work in 47 137/191 days or 47.717 days Answer
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