Question:
If Ashley can finish the work in 33 days and Eric can finish the same work in 36 days, then in how many days both can finish the work together?
Correct Answer
17 5/23 days or 17.217 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by Ashley = 33 days
And, the number of days to finish the same work by Eric = 36 days
Thus, the number of days to finish the work by Ashley and Eric together = ?
Here,
∵ In 33 days the work done by Ashley = 1
∴ In 1 day, the work done by Ashley = 1/33 part
Similarly,
∵ In 36 days the work done by Eric = 1
∴ In 1 day, the work done by Eric = 1/36 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
= 1/33 + 1/36
= 12 + 11/396
= 23/396 part of work
This means in 1 day, 23/396 part of work is done by Ashley and Eric working together.
Now, the number of days required to finish 23/396 part of work by Ashley + Eric working together = 1
∴ the number of days required to finish 1 work by Ashley + Eric together
= 1/23/396
= 1 × 396/23 = 396/23 days
= 17 5/23 days = or 17.217 days
Thus, Ashley and Eric working together will finish the work in 17 5/23 days = or 17.217 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 = 33 days
And the number of days required to finish the same work by Eric = 36 days
Thus, the number of days required to finish the work Ashley and Eric working together = ?
Here a = 33 days
And, b = 36 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Ashley and Eric working together
= 33 × 36/33 + 36 days
= 1188/69 days
= 1188 ÷ 3/69 ÷ 3 = 396/23 days
= 17 5/23 days or 17.217
Thus, Ashley and Eric together will finish the work in 17 5/23 days or 17.217 days Answer
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