Question : Amy can finish a work in 68 days. Shirley can finish the same work in 73 days while Anna can finish the work in 78 days. How long will it take to finish it if they work together?
Correct Answer 24 2052/7981 days or 24.257 days
Solution & Explanation
Solution
Given,
The number of days required to finish a piece of work by Amy = 68 days
And, the number of days required to finish the same work by Shirley = 73 days
And, the number of days required to finish the same work by Anna = 78 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 68 days the work is done by Amy = 1
∴ The work done by Amy in 1 day = 1/68
Similarly,
∵ In 73 days the work is done by Shirley = 1
∴ The work done by Shirley in 1 day = 1/73
Similarly,
∵ In 78 days the work is done by Anna = 1
∴ The work done by Anna in 1 day = 1/78 part
Now, the work done by Amy, Shirley, and Anna together in 1 day
= Amy's 1 day work + Shirley's 1 day work + Anna's 1 day work
= 1/68 + 1/73 + 1/78
= 2847 + 2652 + 2482/193596
= 7981/193596 part of work
This means in 1 day, 7981/193596 part of work is done by Amy, Shirley and Anna working together.
Now, the number of days required to finish 7981/193596 part of work by Amy, Shirley, and Anna working together = 1
∴ the number of days required to finish the whole work (1 work) by Amy + Shirley + Anna together
= 1/7981/193596
= 1 × 193596/7981 = 193596/7981 days
= 24 2052/7981 days = or 24.257 days
Thus, Amy, Shirley, and Anna working together will finish the total work (1 work) in 24 2052/7981 days = or 24.257 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, B can finish the same work in b days, and C can finish the work in c days
then working together the number of days required to finish the work
= a × b × c/ab + ac + bc 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 Shirley = 73 days
And the number of days required to finish the work by Anna = 78 days
Thus, the number of days required to finish the work by Amy, Shirley, and Anna together = ?
Here a = 68 days
And, b = 73 days
And, c = 78 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Amy, Shirley, and Anna working together
= 68 × 73 × 78/68 × 73 + 68 × 78 + 73 × 78 days
= 387192/4964 + 5304 + 5694 days
= 387192/15962 days
= 387192/15962 days
= 387192 ÷ 2/15962 ÷ 2 = 193596/7981 days
= 24 2052/7981 days or 24.257
Thus, Amy, Shirley, and Anna together will finish the work in 24 2052/7981 days or 24.257 days Answer
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