Question:
If Ashley can finish the work in 36 days and Eric can finish the same work in 41 days, then in how many days both can finish the work together?
Correct Answer
19 13/77 days or 19.169 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by Ashley = 36 days
And, the number of days to finish the same work by Eric = 41 days
Thus, the number of days to finish the work by Ashley and Eric together = ?
Here,
∵ In 36 days the work done by Ashley = 1
∴ In 1 day, the work done by Ashley = 1/36 part
Similarly,
∵ In 41 days the work done by Eric = 1
∴ In 1 day, the work done by Eric = 1/41 part
Now, in 1 day, the work done by Ashley and Eric together
= In 1 day work done by Ashley + In 1 day the work done by Eric
= 1/36 + 1/41
= 41 + 36/1476
= 77/1476 part of work
This means in 1 day, 77/1476 part of work is done by Ashley and Eric working together.
Now, the number of days required to finish 77/1476 part of work by Ashley + Eric working together = 1
∴ the number of days required to finish 1 work by Ashley + Eric together
= 1/77/1476
= 1 × 1476/77 = 1476/77 days
= 19 13/77 days = or 19.169 days
Thus, Ashley and Eric working together will finish the work in 19 13/77 days = or 19.169 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 Ashley = 36 days
And the number of days required to finish the same work by Eric = 41 days
Thus, the number of days required to finish the work Ashley and Eric working together = ?
Here a = 36 days
And, b = 41 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Ashley and Eric working together
= 36 × 41/36 + 41 days
= 1476/77 days
= 19 13/77 days or 19.169
Thus, Ashley and Eric together will finish the work in 19 13/77 days or 19.169 days Answer
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