Question:
If Jeffrey can finish the work in 61 days and Peter can finish the same work in 66 days, then in how many days both can finish the work together?
Correct Answer
31 89/127 days or 31.701 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by Jeffrey = 61 days
And, the number of days to finish the same work by Peter = 66 days
Thus, the number of days to finish the work by Jeffrey and Peter together = ?
Here,
∵ In 61 days the work done by Jeffrey = 1
∴ In 1 day, the work done by Jeffrey = 1/61 part
Similarly,
∵ In 66 days the work done by Peter = 1
∴ In 1 day, the work done by Peter = 1/66 part
Now, in 1 day, the work done by Jeffrey and Peter together
= In 1 day work done by Jeffrey + In 1 day the work done by Peter
= 1/61 + 1/66
= 66 + 61/4026
= 127/4026 part of work
This means in 1 day, 127/4026 part of work is done by Jeffrey and Peter working together.
Now, the number of days required to finish 127/4026 part of work by Jeffrey + Peter working together = 1
∴ the number of days required to finish 1 work by Jeffrey + Peter together
= 1/127/4026
= 1 × 4026/127 = 4026/127 days
= 31 89/127 days = or 31.701 days
Thus, Jeffrey and Peter working together will finish the work in 31 89/127 days = or 31.701 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 Jeffrey = 61 days
And the number of days required to finish the same work by Peter = 66 days
Thus, the number of days required to finish the work Jeffrey and Peter working together = ?
Here a = 61 days
And, b = 66 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Jeffrey and Peter working together
= 61 × 66/61 + 66 days
= 4026/127 days
= 31 89/127 days or 31.701
Thus, Jeffrey and Peter together will finish the work in 31 89/127 days or 31.701 days Answer
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