Question : Karen can finish a work in 20 days. Lisa can finish the same work in 21 days while Nancy can finish the work in 22 days. How long will it take to finish it if they work together?
Correct Answer 6 654/661 days or 6.989 days
Solution & Explanation
Solution
Given,
The number of days required to finish a piece of work by Karen = 20 days
And, the number of days required to finish the same work by Lisa = 21 days
And, the number of days required to finish the same work by Nancy = 22 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 20 days the work is done by Karen = 1
∴ The work done by Karen in 1 day = 1/20
Similarly,
∵ In 21 days the work is done by Lisa = 1
∴ The work done by Lisa in 1 day = 1/21
Similarly,
∵ In 22 days the work is done by Nancy = 1
∴ The work done by Nancy in 1 day = 1/22 part
Now, the work done by Karen, Lisa, and Nancy together in 1 day
= Karen's 1 day work + Lisa's 1 day work + Nancy's 1 day work
= 1/20 + 1/21 + 1/22
= 231 + 220 + 210/4620
= 661/4620 part of work
This means in 1 day, 661/4620 part of work is done by Karen, Lisa and Nancy working together.
Now, the number of days required to finish 661/4620 part of work by Karen, Lisa, and Nancy working together = 1
∴ the number of days required to finish the whole work (1 work) by Karen + Lisa + Nancy together
= 1/661/4620
= 1 × 4620/661 = 4620/661 days
= 6 654/661 days = or 6.989 days
Thus, Karen, Lisa, and Nancy working together will finish the total work (1 work) in 6 654/661 days = or 6.989 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 Karen = 20 days
And the number of days required to finish the same work by Lisa = 21 days
And the number of days required to finish the work by Nancy = 22 days
Thus, the number of days required to finish the work by Karen, Lisa, and Nancy together = ?
Here a = 20 days
And, b = 21 days
And, c = 22 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Karen, Lisa, and Nancy working together
= 20 × 21 × 22/20 × 21 + 20 × 22 + 21 × 22 days
= 9240/420 + 440 + 462 days
= 9240/1322 days
= 9240/1322 days
= 9240 ÷ 2/1322 ÷ 2 = 4620/661 days
= 6 654/661 days or 6.989
Thus, Karen, Lisa, and Nancy together will finish the work in 6 654/661 days or 6.989 days Answer
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