Question:
If Carol can finish the work in 43 days and Alexander can finish the same work in 46 days, then in how many days both can finish the work together?
Correct Answer
22 20/89 days or 22.225 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by Carol = 43 days
And, the number of days to finish the same work by Alexander = 46 days
Thus, the number of days to finish the work by Carol and Alexander together = ?
Here,
∵ In 43 days the work done by Carol = 1
∴ In 1 day, the work done by Carol = 1/43 part
Similarly,
∵ In 46 days the work done by Alexander = 1
∴ In 1 day, the work done by Alexander = 1/46 part
Now, in 1 day, the work done by Carol and Alexander together
= In 1 day work done by Carol + In 1 day the work done by Alexander
= 1/43 + 1/46
= 46 + 43/1978
= 89/1978 part of work
This means in 1 day, 89/1978 part of work is done by Carol and Alexander working together.
Now, the number of days required to finish 89/1978 part of work by Carol + Alexander working together = 1
∴ the number of days required to finish 1 work by Carol + Alexander together
= 1/89/1978
= 1 × 1978/89 = 1978/89 days
= 22 20/89 days = or 22.225 days
Thus, Carol and Alexander working together will finish the work in 22 20/89 days = or 22.225 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 Carol = 43 days
And the number of days required to finish the same work by Alexander = 46 days
Thus, the number of days required to finish the work Carol and Alexander working together = ?
Here a = 43 days
And, b = 46 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Carol and Alexander working together
= 43 × 46/43 + 46 days
= 1978/89 days
= 22 20/89 days or 22.225
Thus, Carol and Alexander together will finish the work in 22 20/89 days or 22.225 days Answer
Similar Questions
(1) If Raymond can finish the work in 97 days and Eugene can finish the same work in 102 days, then in how many days both can finish the work together?
(2) If John can finish the work in 9 days and Richard can finish the same work in 14 days, then in how many days both can finish the work together?
(3) Patrick can finish a work in 95 days. Jack can finish the same work in 100 days while Dennis can finish the work in 105 days. How long will it take to finish it if they work together?
(4) Sandra can finish a work in 34 days. Kimberly can finish the same work in 39 days while Emily can finish the work in 44 days. How long will it take to finish it if they work together?
(5) John can finish a work in 5 days. Michael can finish the same work in 6 days while David can finish the work in 7 days. How long will it take to finish it if they work together?
(6) If Kimberly can finish the work in 35 days and Stephen can finish the same work in 38 days, then in how many days both can finish the work together?
(7) Dorothy can finish a work in 50 days. Deborah can finish the same work in 55 days while Stephanie can finish the work in 60 days. How long will it take to finish it if they work together?
(8) If Mary can finish the work in 3 days and Michael can finish the same work in 7 days, then in how many days both can finish the work together?
(9) If Robert can finish the work in 4 days and David can finish the same work in 7 days, then in how many days both can finish the work together?
(10) If Sandra can finish the work in 31 days and Gary can finish the same work in 34 days, then in how many days both can finish the work together?