Question:
If Helen can finish the work in 84 days and Bruce can finish the same work in 89 days, then in how many days both can finish the work together?
Correct Answer
43 37/173 days or 43.214 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by Helen = 84 days
And, the number of days to finish the same work by Bruce = 89 days
Thus, the number of days to finish the work by Helen and Bruce together = ?
Here,
∵ In 84 days the work done by Helen = 1
∴ In 1 day, the work done by Helen = 1/84 part
Similarly,
∵ In 89 days the work done by Bruce = 1
∴ In 1 day, the work done by Bruce = 1/89 part
Now, in 1 day, the work done by Helen and Bruce together
= In 1 day work done by Helen + In 1 day the work done by Bruce
= 1/84 + 1/89
= 89 + 84/7476
= 173/7476 part of work
This means in 1 day, 173/7476 part of work is done by Helen and Bruce working together.
Now, the number of days required to finish 173/7476 part of work by Helen + Bruce working together = 1
∴ the number of days required to finish 1 work by Helen + Bruce together
= 1/173/7476
= 1 × 7476/173 = 7476/173 days
= 43 37/173 days = or 43.214 days
Thus, Helen and Bruce working together will finish the work in 43 37/173 days = or 43.214 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 Helen = 84 days
And the number of days required to finish the same work by Bruce = 89 days
Thus, the number of days required to finish the work Helen and Bruce working together = ?
Here a = 84 days
And, b = 89 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Helen and Bruce working together
= 84 × 89/84 + 89 days
= 7476/173 days
= 43 37/173 days or 43.214
Thus, Helen and Bruce together will finish the work in 43 37/173 days or 43.214 days Answer
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