Question:
If Melissa can finish the work in 49 days and Jerry can finish the same work in 52 days, then in how many days both can finish the work together?
Correct Answer
25 23/101 days or 25.228 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by Melissa = 49 days
And, the number of days to finish the same work by Jerry = 52 days
Thus, the number of days to finish the work by Melissa and Jerry together = ?
Here,
∵ In 49 days the work done by Melissa = 1
∴ In 1 day, the work done by Melissa = 1/49 part
Similarly,
∵ In 52 days the work done by Jerry = 1
∴ In 1 day, the work done by Jerry = 1/52 part
Now, in 1 day, the work done by Melissa and Jerry together
= In 1 day work done by Melissa + In 1 day the work done by Jerry
= 1/49 + 1/52
= 52 + 49/2548
= 101/2548 part of work
This means in 1 day, 101/2548 part of work is done by Melissa and Jerry working together.
Now, the number of days required to finish 101/2548 part of work by Melissa + Jerry working together = 1
∴ the number of days required to finish 1 work by Melissa + Jerry together
= 1/101/2548
= 1 × 2548/101 = 2548/101 days
= 25 23/101 days = or 25.228 days
Thus, Melissa and Jerry working together will finish the work in 25 23/101 days = or 25.228 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 Melissa = 49 days
And the number of days required to finish the same work by Jerry = 52 days
Thus, the number of days required to finish the work Melissa and Jerry working together = ?
Here a = 49 days
And, b = 52 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Melissa and Jerry working together
= 49 × 52/49 + 52 days
= 2548/101 days
= 25 23/101 days or 25.228
Thus, Melissa and Jerry together will finish the work in 25 23/101 days or 25.228 days Answer
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