Question:
If Dorothy can finish the work in 50 days and Jack can finish the same work in 55 days, then in how many days both can finish the work together?
Correct Answer
26 4/21 days or 26.19 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by Dorothy = 50 days
And, the number of days to finish the same work by Jack = 55 days
Thus, the number of days to finish the work by Dorothy and Jack together = ?
Here,
∵ In 50 days the work done by Dorothy = 1
∴ In 1 day, the work done by Dorothy = 1/50 part
Similarly,
∵ In 55 days the work done by Jack = 1
∴ In 1 day, the work done by Jack = 1/55 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
= 1/50 + 1/55
= 11 + 10/550
= 21/550 part of work
This means in 1 day, 21/550 part of work is done by Dorothy and Jack working together.
Now, the number of days required to finish 21/550 part of work by Dorothy + Jack working together = 1
∴ the number of days required to finish 1 work by Dorothy + Jack together
= 1/21/550
= 1 × 550/21 = 550/21 days
= 26 4/21 days = or 26.19 days
Thus, Dorothy and Jack working together will finish the work in 26 4/21 days = or 26.19 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 = 50 days
And the number of days required to finish the same work by Jack = 55 days
Thus, the number of days required to finish the work Dorothy and Jack working together = ?
Here a = 50 days
And, b = 55 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Dorothy and Jack working together
= 50 × 55/50 + 55 days
= 2750/105 days
= 2750 ÷ 5/105 ÷ 5 = 550/21 days
= 26 4/21 days or 26.19
Thus, Dorothy and Jack together will finish the work in 26 4/21 days or 26.19 days Answer
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