Question:
If Samuel can finish the work in 87 days and Albert can finish the same work in 92 days, then in how many days both can finish the work together?
Correct Answer
44 128/179 days or 44.715 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by Samuel = 87 days
And, the number of days to finish the same work by Albert = 92 days
Thus, the number of days to finish the work by Samuel and Albert together = ?
Here,
∵ In 87 days the work done by Samuel = 1
∴ In 1 day, the work done by Samuel = 1/87 part
Similarly,
∵ In 92 days the work done by Albert = 1
∴ In 1 day, the work done by Albert = 1/92 part
Now, in 1 day, the work done by Samuel and Albert together
= In 1 day work done by Samuel + In 1 day the work done by Albert
= 1/87 + 1/92
= 92 + 87/8004
= 179/8004 part of work
This means in 1 day, 179/8004 part of work is done by Samuel and Albert working together.
Now, the number of days required to finish 179/8004 part of work by Samuel + Albert working together = 1
∴ the number of days required to finish 1 work by Samuel + Albert together
= 1/179/8004
= 1 × 8004/179 = 8004/179 days
= 44 128/179 days = or 44.715 days
Thus, Samuel and Albert working together will finish the work in 44 128/179 days = or 44.715 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 Samuel = 87 days
And the number of days required to finish the same work by Albert = 92 days
Thus, the number of days required to finish the work Samuel and Albert working together = ?
Here a = 87 days
And, b = 92 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Samuel and Albert working together
= 87 × 92/87 + 92 days
= 8004/179 days
= 44 128/179 days or 44.715
Thus, Samuel and Albert together will finish the work in 44 128/179 days or 44.715 days Answer
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