Question : If Barbara can finish the work in 35 days and Anthony can finish the same work in 51 days, then in how many days both can finish the work together?
Correct Answer 20 65/86 days or 20.756 days
Solution & Explanation
Solution
Given,
The number of days to finish the work by Barbara = 35 days
And, the number of days to finish the same work by Anthony = 51 days
Thus, the number of days to finish the work by Barbara and Anthony together = ?
Here,
∵ In 35 days the work done by Barbara = 1
∴ In 1 day, the work done by Barbara = 1/35 part
Similarly,
∵ In 51 days the work done by Anthony = 1
∴ In 1 day, the work done by Anthony = 1/51 part
Now, in 1 day, the work done by Barbara and Anthony together
= In 1 day work done by Barbara + In 1 day the work done by Anthony
= 1/35 + 1/51
= 51 + 35/1785
= 86/1785 part of work
This means in 1 day, 86/1785 part of work is done by Barbara and Anthony working together.
Now, the number of days required to finish 86/1785 part of work by Barbara + Anthony working together = 1
∴ the number of days required to finish 1 work by Barbara + Anthony together
= 1/86/1785
= 1 × 1785/86 = 1785/86 days
= 20 65/86 days = or 20.756 days
Thus, Barbara and Anthony working together will finish the work in 20 65/86 days = or 20.756 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 Barbara = 35 days
And the number of days required to finish the same work by Anthony = 51 days
Thus, the number of days required to finish the work Barbara and Anthony working together = ?
Here a = 35 days
And, b = 51 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Barbara and Anthony working together
= 35 × 51/35 + 51 days
= 1785/86 days
= 20 65/86 days or 20.756
Thus, Barbara and Anthony together will finish the work in 20 65/86 days or 20.756 days Answer
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