Question : If Elizabeth can finish the work in 33 days and Daniel can finish the same work in 49 days, then in how many days both can finish the work together?
Correct Answer 19 59/82 days or 19.72 days
Solution & Explanation
Solution
Given,
The number of days to finish the work by Elizabeth = 33 days
And, the number of days to finish the same work by Daniel = 49 days
Thus, the number of days to finish the work by Elizabeth and Daniel together = ?
Here,
∵ In 33 days the work done by Elizabeth = 1
∴ In 1 day, the work done by Elizabeth = 1/33 part
Similarly,
∵ In 49 days the work done by Daniel = 1
∴ In 1 day, the work done by Daniel = 1/49 part
Now, in 1 day, the work done by Elizabeth and Daniel together
= In 1 day work done by Elizabeth + In 1 day the work done by Daniel
= 1/33 + 1/49
= 49 + 33/1617
= 82/1617 part of work
This means in 1 day, 82/1617 part of work is done by Elizabeth and Daniel working together.
Now, the number of days required to finish 82/1617 part of work by Elizabeth + Daniel working together = 1
∴ the number of days required to finish 1 work by Elizabeth + Daniel together
= 1/82/1617
= 1 × 1617/82 = 1617/82 days
= 19 59/82 days = or 19.72 days
Thus, Elizabeth and Daniel working together will finish the work in 19 59/82 days = or 19.72 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 Elizabeth = 33 days
And the number of days required to finish the same work by Daniel = 49 days
Thus, the number of days required to finish the work Elizabeth and Daniel working together = ?
Here a = 33 days
And, b = 49 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Elizabeth and Daniel working together
= 33 × 49/33 + 49 days
= 1617/82 days
= 19 59/82 days or 19.72
Thus, Elizabeth and Daniel together will finish the work in 19 59/82 days or 19.72 days Answer
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