Question : If Amy can finish the work in 68 days and Keith can finish the same work in 73 days, then in how many days both can finish the work together?
Correct Answer 35 29/141 days or 35.206 days
Solution & Explanation
Solution
Given,
The number of days to finish the work by Amy = 68 days
And, the number of days to finish the same work by Keith = 73 days
Thus, the number of days to finish the work by Amy and Keith together = ?
Here,
∵ In 68 days the work done by Amy = 1
∴ In 1 day, the work done by Amy = 1/68 part
Similarly,
∵ In 73 days the work done by Keith = 1
∴ In 1 day, the work done by Keith = 1/73 part
Now, in 1 day, the work done by Amy and Keith together
= In 1 day work done by Amy + In 1 day the work done by Keith
= 1/68 + 1/73
= 73 + 68/4964
= 141/4964 part of work
This means in 1 day, 141/4964 part of work is done by Amy and Keith working together.
Now, the number of days required to finish 141/4964 part of work by Amy + Keith working together = 1
∴ the number of days required to finish 1 work by Amy + Keith together
= 1/141/4964
= 1 × 4964/141 = 4964/141 days
= 35 29/141 days = or 35.206 days
Thus, Amy and Keith working together will finish the work in 35 29/141 days = or 35.206 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 Amy = 68 days
And the number of days required to finish the same work by Keith = 73 days
Thus, the number of days required to finish the work Amy and Keith working together = ?
Here a = 68 days
And, b = 73 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Amy and Keith working together
= 68 × 73/68 + 73 days
= 4964/141 days
= 35 29/141 days or 35.206
Thus, Amy and Keith together will finish the work in 35 29/141 days or 35.206 days Answer
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