Question:
If Jack can finish the work in 99 days and Bobby can finish the same work in 104 days, then in how many days both can finish the work together?
Correct Answer
50 146/203 days or 50.719 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by Jack = 99 days
And, the number of days to finish the same work by Bobby = 104 days
Thus, the number of days to finish the work by Jack and Bobby together = ?
Here,
∵ In 99 days the work done by Jack = 1
∴ In 1 day, the work done by Jack = 1/99 part
Similarly,
∵ In 104 days the work done by Bobby = 1
∴ In 1 day, the work done by Bobby = 1/104 part
Now, in 1 day, the work done by Jack and Bobby together
= In 1 day work done by Jack + In 1 day the work done by Bobby
= 1/99 + 1/104
= 104 + 99/10296
= 203/10296 part of work
This means in 1 day, 203/10296 part of work is done by Jack and Bobby working together.
Now, the number of days required to finish 203/10296 part of work by Jack + Bobby working together = 1
∴ the number of days required to finish 1 work by Jack + Bobby together
= 1/203/10296
= 1 × 10296/203 = 10296/203 days
= 50 146/203 days = or 50.719 days
Thus, Jack and Bobby working together will finish the work in 50 146/203 days = or 50.719 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 Jack = 99 days
And the number of days required to finish the same work by Bobby = 104 days
Thus, the number of days required to finish the work Jack and Bobby working together = ?
Here a = 99 days
And, b = 104 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Jack and Bobby working together
= 99 × 104/99 + 104 days
= 10296/203 days
= 50 146/203 days or 50.719
Thus, Jack and Bobby together will finish the work in 50 146/203 days or 50.719 days Answer
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