Question:
If Patrick can finish the work in 95 days and Vincent can finish the same work in 100 days, then in how many days both can finish the work together?
Correct Answer
48 28/39 days or 48.718 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by Patrick = 95 days
And, the number of days to finish the same work by Vincent = 100 days
Thus, the number of days to finish the work by Patrick and Vincent together = ?
Here,
∵ In 95 days the work done by Patrick = 1
∴ In 1 day, the work done by Patrick = 1/95 part
Similarly,
∵ In 100 days the work done by Vincent = 1
∴ In 1 day, the work done by Vincent = 1/100 part
Now, in 1 day, the work done by Patrick and Vincent together
= In 1 day work done by Patrick + In 1 day the work done by Vincent
= 1/95 + 1/100
= 20 + 19/1900
= 39/1900 part of work
This means in 1 day, 39/1900 part of work is done by Patrick and Vincent working together.
Now, the number of days required to finish 39/1900 part of work by Patrick + Vincent working together = 1
∴ the number of days required to finish 1 work by Patrick + Vincent together
= 1/39/1900
= 1 × 1900/39 = 1900/39 days
= 48 28/39 days = or 48.718 days
Thus, Patrick and Vincent working together will finish the work in 48 28/39 days = or 48.718 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 Patrick = 95 days
And the number of days required to finish the same work by Vincent = 100 days
Thus, the number of days required to finish the work Patrick and Vincent working together = ?
Here a = 95 days
And, b = 100 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Patrick and Vincent working together
= 95 × 100/95 + 100 days
= 9500/195 days
= 9500 ÷ 5/195 ÷ 5 = 1900/39 days
= 48 28/39 days or 48.718
Thus, Patrick and Vincent together will finish the work in 48 28/39 days or 48.718 days Answer
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