Question:
If Carol can finish the work in 46 days and Alexander can finish the same work in 51 days, then in how many days both can finish the work together?
Correct Answer
24 18/97 days or 24.186 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by Carol = 46 days
And, the number of days to finish the same work by Alexander = 51 days
Thus, the number of days to finish the work by Carol and Alexander together = ?
Here,
∵ In 46 days the work done by Carol = 1
∴ In 1 day, the work done by Carol = 1/46 part
Similarly,
∵ In 51 days the work done by Alexander = 1
∴ In 1 day, the work done by Alexander = 1/51 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
= 1/46 + 1/51
= 51 + 46/2346
= 97/2346 part of work
This means in 1 day, 97/2346 part of work is done by Carol and Alexander working together.
Now, the number of days required to finish 97/2346 part of work by Carol + Alexander working together = 1
∴ the number of days required to finish 1 work by Carol + Alexander together
= 1/97/2346
= 1 × 2346/97 = 2346/97 days
= 24 18/97 days = or 24.186 days
Thus, Carol and Alexander working together will finish the work in 24 18/97 days = or 24.186 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 = 46 days
And the number of days required to finish the same work by Alexander = 51 days
Thus, the number of days required to finish the work Carol and Alexander working together = ?
Here a = 46 days
And, b = 51 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Carol and Alexander working together
= 46 × 51/46 + 51 days
= 2346/97 days
= 24 18/97 days or 24.186
Thus, Carol and Alexander together will finish the work in 24 18/97 days or 24.186 days Answer
Similar Questions
(1) Kenneth can finish a work in 45 days. Brian can finish the same work in 50 days while George can finish the work in 55 days. How long will it take to finish it if they work together?
(2) If Karen can finish the work in 21 days and Kevin can finish the same work in 24 days, then in how many days both can finish the work together?
(3) Laura can finish a work in 62 days. Kathleen can finish the same work in 67 days while Amy can finish the work in 72 days. How long will it take to finish it if they work together?
(4) Susan can finish a work in 18 days. Sarah can finish the same work in 23 days while Karen can finish the work in 28 days. How long will it take to finish it if they work together?
(5) If Michelle can finish the work in 41 days and Samuel can finish the same work in 44 days, then in how many days both can finish the work together?
(6) If A can finish a work in 10 days and B can finish the same work in 15 days, then in how many days they both can finish the work working together?
(7) If Barbara can finish the work in 16 days and Anthony can finish the same work in 21 days, then in how many days both can finish the work together?
(8) If Patricia can finish the work in 5 days and William can finish the same work in 8 days, then in how many days both can finish the work together?
(9) Nancy can finish a work in 28 days. Margaret can finish the same work in 33 days while Sandra can finish the work in 38 days. How long will it take to finish it if they work together?
(10) Michael can finish a work in 11 days. William can finish the same work in 16 days while Richard can finish the work in 21 days. How long will it take to finish it if they work together?