Question:
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?
Correct Answer
11 1/5 days or 11.2 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by Karen = 21 days
And, the number of days to finish the same work by Kevin = 24 days
Thus, the number of days to finish the work by Karen and Kevin together = ?
Here,
∵ In 21 days the work done by Karen = 1
∴ In 1 day, the work done by Karen = 1/21 part
Similarly,
∵ In 24 days the work done by Kevin = 1
∴ In 1 day, the work done by Kevin = 1/24 part
Now, in 1 day, the work done by Karen and Kevin together
= In 1 day work done by Karen + In 1 day the work done by Kevin
= 1/21 + 1/24
= 8 + 7/168
= 15/168 part of work
= 15 ÷ 3/168 ÷ 3 part of work
= 5/56 part of work
This means, in 1 day, 5/56 part of the work is done by Karen and Kevin together.
Now, the number of days required to finish 5/56 part of work by Karen + Kevin working together = 1
∴ the number of days required to finish 1 work by Karen + Kevin together
= 1/5/56
= 1 × 56/5 = 56/5 days
= 11 1/5 days = or 11.2 days
Thus, Karen and Kevin working together will finish the work in 11 1/5 days = or 11.2 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 Karen = 21 days
And the number of days required to finish the same work by Kevin = 24 days
Thus, the number of days required to finish the work Karen and Kevin working together = ?
Here a = 21 days
And, b = 24 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Karen and Kevin working together
= 21 × 24/21 + 24 days
= 504/45 days
= 504 ÷ 9/45 ÷ 9 = 56/5 days
= 11 1/5 days or 11.2
Thus, Karen and Kevin together will finish the work in 11 1/5 days or 11.2 days Answer
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