Question:
If Nicole can finish the work in 82 days and Billy can finish the same work in 87 days, then in how many days both can finish the work together?
Correct Answer
42 36/169 days or 42.213 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by Nicole = 82 days
And, the number of days to finish the same work by Billy = 87 days
Thus, the number of days to finish the work by Nicole and Billy together = ?
Here,
∵ In 82 days the work done by Nicole = 1
∴ In 1 day, the work done by Nicole = 1/82 part
Similarly,
∵ In 87 days the work done by Billy = 1
∴ In 1 day, the work done by Billy = 1/87 part
Now, in 1 day, the work done by Nicole and Billy together
= In 1 day work done by Nicole + In 1 day the work done by Billy
= 1/82 + 1/87
= 87 + 82/7134
= 169/7134 part of work
This means in 1 day, 169/7134 part of work is done by Nicole and Billy working together.
Now, the number of days required to finish 169/7134 part of work by Nicole + Billy working together = 1
∴ the number of days required to finish 1 work by Nicole + Billy together
= 1/169/7134
= 1 × 7134/169 = 7134/169 days
= 42 36/169 days = or 42.213 days
Thus, Nicole and Billy working together will finish the work in 42 36/169 days = or 42.213 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 Nicole = 82 days
And the number of days required to finish the same work by Billy = 87 days
Thus, the number of days required to finish the work Nicole and Billy working together = ?
Here a = 82 days
And, b = 87 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Nicole and Billy working together
= 82 × 87/82 + 87 days
= 7134/169 days
= 42 36/169 days or 42.213
Thus, Nicole and Billy together will finish the work in 42 36/169 days or 42.213 days Answer
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