Question:
If Edward can finish the work in 57 days and Nathan can finish the same work in 62 days, then in how many days both can finish the work together?
Correct Answer
29 83/119 days or 29.697 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by Edward = 57 days
And, the number of days to finish the same work by Nathan = 62 days
Thus, the number of days to finish the work by Edward and Nathan together = ?
Here,
∵ In 57 days the work done by Edward = 1
∴ In 1 day, the work done by Edward = 1/57 part
Similarly,
∵ In 62 days the work done by Nathan = 1
∴ In 1 day, the work done by Nathan = 1/62 part
Now, in 1 day, the work done by Edward and Nathan together
= In 1 day work done by Edward + In 1 day the work done by Nathan
= 1/57 + 1/62
= 62 + 57/3534
= 119/3534 part of work
This means in 1 day, 119/3534 part of work is done by Edward and Nathan working together.
Now, the number of days required to finish 119/3534 part of work by Edward + Nathan working together = 1
∴ the number of days required to finish 1 work by Edward + Nathan together
= 1/119/3534
= 1 × 3534/119 = 3534/119 days
= 29 83/119 days = or 29.697 days
Thus, Edward and Nathan working together will finish the work in 29 83/119 days = or 29.697 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 Edward = 57 days
And the number of days required to finish the same work by Nathan = 62 days
Thus, the number of days required to finish the work Edward and Nathan working together = ?
Here a = 57 days
And, b = 62 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Edward and Nathan working together
= 57 × 62/57 + 62 days
= 3534/119 days
= 29 83/119 days or 29.697
Thus, Edward and Nathan together will finish the work in 29 83/119 days or 29.697 days Answer
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