Question:
If Patricia can finish the work in 5 days and William can finish the same work in 8 days, then in how many days both can finish the work together?
Correct Answer
3 1/13 days or 3.077 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by Patricia = 5 days
And, the number of days to finish the same work by William = 8 days
Thus, the number of days to finish the work by Patricia and William together = ?
Here,
∵ In 5 days the work done by Patricia = 1
∴ In 1 day, the work done by Patricia = 1/5 part
Similarly,
∵ In 8 days the work done by William = 1
∴ In 1 day, the work done by William = 1/8 part
Now, in 1 day, the work done by Patricia and William together
= In 1 day work done by Patricia + In 1 day the work done by William
= 1/5 + 1/8
= 8 + 5/40
= 13/40 part of work
This means in 1 day, 13/40 part of work is done by Patricia and William working together.
Now, the number of days required to finish 13/40 part of work by Patricia + William working together = 1
∴ the number of days required to finish 1 work by Patricia + William together
= 1/13/40
= 1 × 40/13 = 40/13 days
= 3 1/13 days = or 3.077 days
Thus, Patricia and William working together will finish the work in 3 1/13 days = or 3.077 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 Patricia = 5 days
And the number of days required to finish the same work by William = 8 days
Thus, the number of days required to finish the work Patricia and William working together = ?
Here a = 5 days
And, b = 8 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Patricia and William working together
= 5 × 8/5 + 8 days
= 40/13 days
= 3 1/13 days or 3.077
Thus, Patricia and William together will finish the work in 3 1/13 days or 3.077 days Answer
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