Question:
If Dorothy can finish the work in 47 days and Jack can finish the same work in 50 days, then in how many days both can finish the work together?
Correct Answer
24 22/97 days or 24.227 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 = 50 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 50 days the work done by Jack = 1
∴ In 1 day, the work done by Jack = 1/50 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 + 1/50
= 50 + 47/2350
= 97/2350 part of work
This means in 1 day, 97/2350 part of work is done by Dorothy and Jack working together.
Now, the number of days required to finish 97/2350 part of work by Dorothy + Jack working together = 1
∴ the number of days required to finish 1 work by Dorothy + Jack together
= 1/97/2350
= 1 × 2350/97 = 2350/97 days
= 24 22/97 days = or 24.227 days
Thus, Dorothy and Jack working together will finish the work in 24 22/97 days = or 24.227 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 = 50 days
Thus, the number of days required to finish the work Dorothy and Jack working together = ?
Here a = 47 days
And, b = 50 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 × 50/47 + 50 days
= 2350/97 days
= 24 22/97 days or 24.227
Thus, Dorothy and Jack together will finish the work in 24 22/97 days or 24.227 days Answer
Similar Questions
(1) If Brenda can finish the work in 76 days and Arthur can finish the same work in 81 days, then in how many days both can finish the work together?
(2) Emma can finish a work in 80 days. Helen can finish the same work in 85 days while Samantha can finish the work in 90 days. How long will it take to finish it if they work together?
(3) If Christine can finish the work in 90 days and Juan can finish the same work in 95 days, then in how many days both can finish the work together?
(4) If Elizabeth can finish the work in 11 days and Daniel can finish the same work in 15 days, then in how many days both can finish the work together?
(5) Helen can finish a work in 84 days. Katherine can finish the same work in 89 days while Christine can finish the work in 94 days. How long will it take to finish it if they work together?
(6) If Jacob can finish the work in 65 days and Noah can finish the same work in 70 days, then in how many days both can finish the work together?
(7) If Jack can finish the work in 99 days and Bobby can finish the same work in 104 days, then in how many days both can finish the work together?
(8) If Donald can finish the work in 32 days and Nicholas can finish the same work in 36 days, then in how many days both can finish the work together?
(9) Emily can finish a work in 40 days. Michelle can finish the same work in 45 days while Carol can finish the work in 50 days. How long will it take to finish it if they work together?
(10) If Sharon can finish the work in 60 days and Zachary can finish the same work in 65 days, then in how many days both can finish the work together?