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) 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?
(2) If Amanda can finish the work in 45 days and Patrick can finish the same work in 48 days, then in how many days both can finish the work together?
(3) If Emily can finish the work in 40 days and Justin can finish the same work in 45 days, then in how many days both can finish the work together?
(4) If Rebecca can finish the work in 58 days and Henry can finish the same work in 63 days, then in how many days both can finish the work together?
(5) If Michael can finish the work in 11 days and Thomas can finish the same work in 16 days, then in how many days both can finish the work together?
(6) Melissa can finish a work in 48 days. Deborah can finish the same work in 49 days while Stephanie can finish the work in 50 days. How long will it take to finish it if they work together?
(7) If Robert can finish a work in 5 days and Bob can finish the same work in 6 days, then in how many days they both can finish the work working together?
(8) 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?
(9) Jeffrey can finish a work in 61 days. Jacob can finish the same work in 66 days while Gary can finish the work in 71 days. How long will it take to finish it if they work together?
(10) If Charles can finish the work in 20 days and Kenneth can finish the same work in 23 days, then in how many days both can finish the work together?