Question : If Margaret can finish the work in 32 days and Ryan can finish the same work in 37 days, then in how many days both can finish the work together?
Correct Answer 17 11/69 days or 17.159 days
Solution & Explanation
Solution
Given,
The number of days to finish the work by Margaret = 32 days
And, the number of days to finish the same work by Ryan = 37 days
Thus, the number of days to finish the work by Margaret and Ryan together = ?
Here,
∵ In 32 days the work done by Margaret = 1
∴ In 1 day, the work done by Margaret = 1/32 part
Similarly,
∵ In 37 days the work done by Ryan = 1
∴ In 1 day, the work done by Ryan = 1/37 part
Now, in 1 day, the work done by Margaret and Ryan together
= In 1 day work done by Margaret + In 1 day the work done by Ryan
= 1/32 + 1/37
= 37 + 32/1184
= 69/1184 part of work
This means in 1 day, 69/1184 part of work is done by Margaret and Ryan working together.
Now, the number of days required to finish 69/1184 part of work by Margaret + Ryan working together = 1
∴ the number of days required to finish 1 work by Margaret + Ryan together
= 1/69/1184
= 1 × 1184/69 = 1184/69 days
= 17 11/69 days = or 17.159 days
Thus, Margaret and Ryan working together will finish the work in 17 11/69 days = or 17.159 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 Margaret = 32 days
And the number of days required to finish the same work by Ryan = 37 days
Thus, the number of days required to finish the work Margaret and Ryan working together = ?
Here a = 32 days
And, b = 37 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Margaret and Ryan working together
= 32 × 37/32 + 37 days
= 1184/69 days
= 17 11/69 days or 17.159
Thus, Margaret and Ryan together will finish the work in 17 11/69 days or 17.159 days Answer
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