Question:
If Patricia can finish the work in 8 days and William can finish the same work in 13 days, then in how many days both can finish the work together?
Correct Answer
4 20/21 days or 4.952 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by Patricia = 8 days
And, the number of days to finish the same work by William = 13 days
Thus, the number of days to finish the work by Patricia and William together = ?
Here,
∵ In 8 days the work done by Patricia = 1
∴ In 1 day, the work done by Patricia = 1/8 part
Similarly,
∵ In 13 days the work done by William = 1
∴ In 1 day, the work done by William = 1/13 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
= 1/8 + 1/13
= 13 + 8/104
= 21/104 part of work
This means in 1 day, 21/104 part of work is done by Patricia and William working together.
Now, the number of days required to finish 21/104 part of work by Patricia + William working together = 1
∴ the number of days required to finish 1 work by Patricia + William together
= 1/21/104
= 1 × 104/21 = 104/21 days
= 4 20/21 days = or 4.952 days
Thus, Patricia and William working together will finish the work in 4 20/21 days = or 4.952 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 = 8 days
And the number of days required to finish the same work by William = 13 days
Thus, the number of days required to finish the work Patricia and William working together = ?
Here a = 8 days
And, b = 13 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Patricia and William working together
= 8 × 13/8 + 13 days
= 104/21 days
= 4 20/21 days or 4.952
Thus, Patricia and William together will finish the work in 4 20/21 days or 4.952 days Answer
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