Question:
If Kevin can finish the work in 47 days and Frank can finish the same work in 52 days, then in how many days both can finish the work together?
Correct Answer
24 68/99 days or 24.687 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by Kevin = 47 days
And, the number of days to finish the same work by Frank = 52 days
Thus, the number of days to finish the work by Kevin and Frank together = ?
Here,
∵ In 47 days the work done by Kevin = 1
∴ In 1 day, the work done by Kevin = 1/47 part
Similarly,
∵ In 52 days the work done by Frank = 1
∴ In 1 day, the work done by Frank = 1/52 part
Now, in 1 day, the work done by Kevin and Frank together
= In 1 day work done by Kevin + In 1 day the work done by Frank
= 1/47 + 1/52
= 52 + 47/2444
= 99/2444 part of work
This means in 1 day, 99/2444 part of work is done by Kevin and Frank working together.
Now, the number of days required to finish 99/2444 part of work by Kevin + Frank working together = 1
∴ the number of days required to finish 1 work by Kevin + Frank together
= 1/99/2444
= 1 × 2444/99 = 2444/99 days
= 24 68/99 days = or 24.687 days
Thus, Kevin and Frank working together will finish the work in 24 68/99 days = or 24.687 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 Kevin = 47 days
And the number of days required to finish the same work by Frank = 52 days
Thus, the number of days required to finish the work Kevin and Frank working together = ?
Here a = 47 days
And, b = 52 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Kevin and Frank working together
= 47 × 52/47 + 52 days
= 2444/99 days
= 24 68/99 days or 24.687
Thus, Kevin and Frank together will finish the work in 24 68/99 days or 24.687 days Answer
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