Question:
If Benjamin can finish the work in 85 days and Gabriel can finish the same work in 90 days, then in how many days both can finish the work together?
Correct Answer
43 5/7 days or 43.714 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by Benjamin = 85 days
And, the number of days to finish the same work by Gabriel = 90 days
Thus, the number of days to finish the work by Benjamin and Gabriel together = ?
Here,
∵ In 85 days the work done by Benjamin = 1
∴ In 1 day, the work done by Benjamin = 1/85 part
Similarly,
∵ In 90 days the work done by Gabriel = 1
∴ In 1 day, the work done by Gabriel = 1/90 part
Now, in 1 day, the work done by Benjamin and Gabriel together
= In 1 day work done by Benjamin + In 1 day the work done by Gabriel
= 1/85 + 1/90
= 18 + 17/1530
= 35/1530 part of work
= 35 ÷ 5/1530 ÷ 5 part of work
= 7/306 part of work
This means, in 1 day, 7/306 part of the work is done by Benjamin and Gabriel together.
Now, the number of days required to finish 7/306 part of work by Benjamin + Gabriel working together = 1
∴ the number of days required to finish 1 work by Benjamin + Gabriel together
= 1/7/306
= 1 × 306/7 = 306/7 days
= 43 5/7 days = or 43.714 days
Thus, Benjamin and Gabriel working together will finish the work in 43 5/7 days = or 43.714 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 Benjamin = 85 days
And the number of days required to finish the same work by Gabriel = 90 days
Thus, the number of days required to finish the work Benjamin and Gabriel working together = ?
Here a = 85 days
And, b = 90 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Benjamin and Gabriel working together
= 85 × 90/85 + 90 days
= 7650/175 days
= 7650 ÷ 25/175 ÷ 25 = 306/7 days
= 43 5/7 days or 43.714
Thus, Benjamin and Gabriel together will finish the work in 43 5/7 days or 43.714 days Answer
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