Question:
If Anna can finish the work in 74 days and Austin can finish the same work in 79 days, then in how many days both can finish the work together?
Correct Answer
38 32/153 days or 38.209 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by Anna = 74 days
And, the number of days to finish the same work by Austin = 79 days
Thus, the number of days to finish the work by Anna and Austin together = ?
Here,
∵ In 74 days the work done by Anna = 1
∴ In 1 day, the work done by Anna = 1/74 part
Similarly,
∵ In 79 days the work done by Austin = 1
∴ In 1 day, the work done by Austin = 1/79 part
Now, in 1 day, the work done by Anna and Austin together
= In 1 day work done by Anna + In 1 day the work done by Austin
= 1/74 + 1/79
= 79 + 74/5846
= 153/5846 part of work
This means in 1 day, 153/5846 part of work is done by Anna and Austin working together.
Now, the number of days required to finish 153/5846 part of work by Anna + Austin working together = 1
∴ the number of days required to finish 1 work by Anna + Austin together
= 1/153/5846
= 1 × 5846/153 = 5846/153 days
= 38 32/153 days = or 38.209 days
Thus, Anna and Austin working together will finish the work in 38 32/153 days = or 38.209 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 Anna = 74 days
And the number of days required to finish the same work by Austin = 79 days
Thus, the number of days required to finish the work Anna and Austin working together = ?
Here a = 74 days
And, b = 79 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Anna and Austin working together
= 74 × 79/74 + 79 days
= 5846/153 days
= 38 32/153 days or 38.209
Thus, Anna and Austin together will finish the work in 38 32/153 days or 38.209 days Answer
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