Question : If Daniel can finish the work in 27 days and Timothy can finish the same work in 32 days, then in how many days both can finish the work together?
Correct Answer 14 38/59 days or 14.644 days
Solution & Explanation
Solution
Given,
The number of days to finish the work by Daniel = 27 days
And, the number of days to finish the same work by Timothy = 32 days
Thus, the number of days to finish the work by Daniel and Timothy together = ?
Here,
∵ In 27 days the work done by Daniel = 1
∴ In 1 day, the work done by Daniel = 1/27 part
Similarly,
∵ In 32 days the work done by Timothy = 1
∴ In 1 day, the work done by Timothy = 1/32 part
Now, in 1 day, the work done by Daniel and Timothy together
= In 1 day work done by Daniel + In 1 day the work done by Timothy
= 1/27 + 1/32
= 32 + 27/864
= 59/864 part of work
This means in 1 day, 59/864 part of work is done by Daniel and Timothy working together.
Now, the number of days required to finish 59/864 part of work by Daniel + Timothy working together = 1
∴ the number of days required to finish 1 work by Daniel + Timothy together
= 1/59/864
= 1 × 864/59 = 864/59 days
= 14 38/59 days = or 14.644 days
Thus, Daniel and Timothy working together will finish the work in 14 38/59 days = or 14.644 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 Daniel = 27 days
And the number of days required to finish the same work by Timothy = 32 days
Thus, the number of days required to finish the work Daniel and Timothy working together = ?
Here a = 27 days
And, b = 32 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Daniel and Timothy working together
= 27 × 32/27 + 32 days
= 864/59 days
= 14 38/59 days or 14.644
Thus, Daniel and Timothy together will finish the work in 14 38/59 days or 14.644 days Answer
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