Question : If Ryan can finish the work in 63 days and Ethan can finish the same work in 68 days, then in how many days both can finish the work together?
Correct Answer 32 92/131 days or 32.702 days
Solution & Explanation
Solution
Given,
The number of days to finish the work by Ryan = 63 days
And, the number of days to finish the same work by Ethan = 68 days
Thus, the number of days to finish the work by Ryan and Ethan together = ?
Here,
∵ In 63 days the work done by Ryan = 1
∴ In 1 day, the work done by Ryan = 1/63 part
Similarly,
∵ In 68 days the work done by Ethan = 1
∴ In 1 day, the work done by Ethan = 1/68 part
Now, in 1 day, the work done by Ryan and Ethan together
= In 1 day work done by Ryan + In 1 day the work done by Ethan
= 1/63 + 1/68
= 68 + 63/4284
= 131/4284 part of work
This means in 1 day, 131/4284 part of work is done by Ryan and Ethan working together.
Now, the number of days required to finish 131/4284 part of work by Ryan + Ethan working together = 1
∴ the number of days required to finish 1 work by Ryan + Ethan together
= 1/131/4284
= 1 × 4284/131 = 4284/131 days
= 32 92/131 days = or 32.702 days
Thus, Ryan and Ethan working together will finish the work in 32 92/131 days = or 32.702 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 Ryan = 63 days
And the number of days required to finish the same work by Ethan = 68 days
Thus, the number of days required to finish the work Ryan and Ethan working together = ?
Here a = 63 days
And, b = 68 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Ryan and Ethan working together
= 63 × 68/63 + 68 days
= 4284/131 days
= 32 92/131 days or 32.702
Thus, Ryan and Ethan together will finish the work in 32 92/131 days or 32.702 days Answer
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