Question:
If Scott can finish the work in 81 days and Bryan can finish the same work in 86 days, then in how many days both can finish the work together?
Correct Answer
41 119/167 days or 41.713 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by Scott = 81 days
And, the number of days to finish the same work by Bryan = 86 days
Thus, the number of days to finish the work by Scott and Bryan together = ?
Here,
∵ In 81 days the work done by Scott = 1
∴ In 1 day, the work done by Scott = 1/81 part
Similarly,
∵ In 86 days the work done by Bryan = 1
∴ In 1 day, the work done by Bryan = 1/86 part
Now, in 1 day, the work done by Scott and Bryan together
= In 1 day work done by Scott + In 1 day the work done by Bryan
= 1/81 + 1/86
= 86 + 81/6966
= 167/6966 part of work
This means in 1 day, 167/6966 part of work is done by Scott and Bryan working together.
Now, the number of days required to finish 167/6966 part of work by Scott + Bryan working together = 1
∴ the number of days required to finish 1 work by Scott + Bryan together
= 1/167/6966
= 1 × 6966/167 = 6966/167 days
= 41 119/167 days = or 41.713 days
Thus, Scott and Bryan working together will finish the work in 41 119/167 days = or 41.713 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 Scott = 81 days
And the number of days required to finish the same work by Bryan = 86 days
Thus, the number of days required to finish the work Scott and Bryan working together = ?
Here a = 81 days
And, b = 86 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Scott and Bryan working together
= 81 × 86/81 + 86 days
= 6966/167 days
= 41 119/167 days or 41.713
Thus, Scott and Bryan together will finish the work in 41 119/167 days or 41.713 days Answer
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