Question:
If Dorothy can finish the work in 47 days and Jack can finish the same work in 51 days, then in how many days both can finish the work together?
Correct Answer
24 45/98 days or 24.459 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by Dorothy = 47 days
And, the number of days to finish the same work by Jack = 51 days
Thus, the number of days to finish the work by Dorothy and Jack together = ?
Here,
∵ In 47 days the work done by Dorothy = 1
∴ In 1 day, the work done by Dorothy = 1/47 part
Similarly,
∵ In 51 days the work done by Jack = 1
∴ In 1 day, the work done by Jack = 1/51 part
Now, in 1 day, the work done by Dorothy and Jack together
= In 1 day work done by Dorothy + In 1 day the work done by Jack
= 1/47 + 1/51
= 51 + 47/2397
= 98/2397 part of work
This means in 1 day, 98/2397 part of work is done by Dorothy and Jack working together.
Now, the number of days required to finish 98/2397 part of work by Dorothy + Jack working together = 1
∴ the number of days required to finish 1 work by Dorothy + Jack together
= 1/98/2397
= 1 × 2397/98 = 2397/98 days
= 24 45/98 days = or 24.459 days
Thus, Dorothy and Jack working together will finish the work in 24 45/98 days = or 24.459 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 Dorothy = 47 days
And the number of days required to finish the same work by Jack = 51 days
Thus, the number of days required to finish the work Dorothy and Jack working together = ?
Here a = 47 days
And, b = 51 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Dorothy and Jack working together
= 47 × 51/47 + 51 days
= 2397/98 days
= 24 45/98 days or 24.459
Thus, Dorothy and Jack together will finish the work in 24 45/98 days or 24.459 days Answer
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