Question:
If Carolyn can finish the work in 96 days and Ralph can finish the same work in 101 days, then in how many days both can finish the work together?
Correct Answer
49 43/197 days or 49.218 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by Carolyn = 96 days
And, the number of days to finish the same work by Ralph = 101 days
Thus, the number of days to finish the work by Carolyn and Ralph together = ?
Here,
∵ In 96 days the work done by Carolyn = 1
∴ In 1 day, the work done by Carolyn = 1/96 part
Similarly,
∵ In 101 days the work done by Ralph = 1
∴ In 1 day, the work done by Ralph = 1/101 part
Now, in 1 day, the work done by Carolyn and Ralph together
= In 1 day work done by Carolyn + In 1 day the work done by Ralph
= 1/96 + 1/101
= 101 + 96/9696
= 197/9696 part of work
This means in 1 day, 197/9696 part of work is done by Carolyn and Ralph working together.
Now, the number of days required to finish 197/9696 part of work by Carolyn + Ralph working together = 1
∴ the number of days required to finish 1 work by Carolyn + Ralph together
= 1/197/9696
= 1 × 9696/197 = 9696/197 days
= 49 43/197 days = or 49.218 days
Thus, Carolyn and Ralph working together will finish the work in 49 43/197 days = or 49.218 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 Carolyn = 96 days
And the number of days required to finish the same work by Ralph = 101 days
Thus, the number of days required to finish the work Carolyn and Ralph working together = ?
Here a = 96 days
And, b = 101 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Carolyn and Ralph working together
= 96 × 101/96 + 101 days
= 9696/197 days
= 49 43/197 days or 49.218
Thus, Carolyn and Ralph together will finish the work in 49 43/197 days or 49.218 days Answer
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