Question : If Melissa can finish the work in 52 days and Jerry can finish the same work in 57 days, then in how many days both can finish the work together?
Correct Answer 27 21/109 days or 27.193 days
Solution & Explanation
Solution
Given,
The number of days to finish the work by Melissa = 52 days
And, the number of days to finish the same work by Jerry = 57 days
Thus, the number of days to finish the work by Melissa and Jerry together = ?
Here,
∵ In 52 days the work done by Melissa = 1
∴ In 1 day, the work done by Melissa = 1/52 part
Similarly,
∵ In 57 days the work done by Jerry = 1
∴ In 1 day, the work done by Jerry = 1/57 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
= 1/52 + 1/57
= 57 + 52/2964
= 109/2964 part of work
This means in 1 day, 109/2964 part of work is done by Melissa and Jerry working together.
Now, the number of days required to finish 109/2964 part of work by Melissa + Jerry working together = 1
∴ the number of days required to finish 1 work by Melissa + Jerry together
= 1/109/2964
= 1 × 2964/109 = 2964/109 days
= 27 21/109 days = or 27.193 days
Thus, Melissa and Jerry working together will finish the work in 27 21/109 days = or 27.193 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 = 52 days
And the number of days required to finish the same work by Jerry = 57 days
Thus, the number of days required to finish the work Melissa and Jerry working together = ?
Here a = 52 days
And, b = 57 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Melissa and Jerry working together
= 52 × 57/52 + 57 days
= 2964/109 days
= 27 21/109 days or 27.193
Thus, Melissa and Jerry together will finish the work in 27 21/109 days or 27.193 days Answer
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