Question : Anna can finish a work in 74 days. Pamela can finish the same work in 79 days while Emma can finish the work in 84 days. How long will it take to finish it if they work together?
Correct Answer 26 2458/9349 days or 26.263 days
Solution & Explanation
Solution
Given,
The number of days required to finish a piece of work by Anna = 74 days
And, the number of days required to finish the same work by Pamela = 79 days
And, the number of days required to finish the same work by Emma = 84 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 74 days the work is done by Anna = 1
∴ The work done by Anna in 1 day = 1/74
Similarly,
∵ In 79 days the work is done by Pamela = 1
∴ The work done by Pamela in 1 day = 1/79
Similarly,
∵ In 84 days the work is done by Emma = 1
∴ The work done by Emma in 1 day = 1/84 part
Now, the work done by Anna, Pamela, and Emma together in 1 day
= Anna's 1 day work + Pamela's 1 day work + Emma's 1 day work
= 1/74 + 1/79 + 1/84
= 3318 + 3108 + 2923/245532
= 9349/245532 part of work
This means in 1 day, 9349/245532 part of work is done by Anna, Pamela and Emma working together.
Now, the number of days required to finish 9349/245532 part of work by Anna, Pamela, and Emma working together = 1
∴ the number of days required to finish the whole work (1 work) by Anna + Pamela + Emma together
= 1/9349/245532
= 1 × 245532/9349 = 245532/9349 days
= 26 2458/9349 days = or 26.263 days
Thus, Anna, Pamela, and Emma working together will finish the total work (1 work) in 26 2458/9349 days = or 26.263 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 Anna = 74 days
And the number of days required to finish the same work by Pamela = 79 days
And the number of days required to finish the work by Emma = 84 days
Thus, the number of days required to finish the work by Anna, Pamela, and Emma together = ?
Here a = 74 days
And, b = 79 days
And, c = 84 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Anna, Pamela, and Emma working together
= 74 × 79 × 84/74 × 79 + 74 × 84 + 79 × 84 days
= 491064/5846 + 6216 + 6636 days
= 491064/18698 days
= 491064/18698 days
= 491064 ÷ 2/18698 ÷ 2 = 245532/9349 days
= 26 2458/9349 days or 26.263
Thus, Anna, Pamela, and Emma together will finish the work in 26 2458/9349 days or 26.263 days Answer
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