Question : Jessica can finish a work in 20 days. Karen can finish the same work in 25 days while Lisa can finish the work in 30 days. How long will it take to finish it if they work together?
Correct Answer 8 4/37 days or 8.108 days
Solution & Explanation
Solution
Given,
The number of days required to finish a piece of work by Jessica = 20 days
And, the number of days required to finish the same work by Karen = 25 days
And, the number of days required to finish the same work by Lisa = 30 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 Jessica = 1
∴ The work done by Jessica in 1 day = 1/20
Similarly,
∵ In 25 days the work is done by Karen = 1
∴ The work done by Karen in 1 day = 1/25
Similarly,
∵ In 30 days the work is done by Lisa = 1
∴ The work done by Lisa in 1 day = 1/30 part
Now, the work done by Jessica, Karen, and Lisa together in 1 day
= Jessica's 1 day work + Karen's 1 day work + Lisa's 1 day work
= 1/20 + 1/25 + 1/30
= 15 + 12 + 10/300
= 37/300 part of work
This means in 1 day, 37/300 part of work is done by Jessica, Karen and Lisa working together.
Now, the number of days required to finish 37/300 part of work by Jessica, Karen, and Lisa working together = 1
∴ the number of days required to finish the whole work (1 work) by Jessica + Karen + Lisa together
= 1/37/300
= 1 × 300/37 = 300/37 days
= 8 4/37 days = or 8.108 days
Thus, Jessica, Karen, and Lisa working together will finish the total work (1 work) in 8 4/37 days = or 8.108 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 Jessica = 20 days
And the number of days required to finish the same work by Karen = 25 days
And the number of days required to finish the work by Lisa = 30 days
Thus, the number of days required to finish the work by Jessica, Karen, and Lisa together = ?
Here a = 20 days
And, b = 25 days
And, c = 30 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Jessica, Karen, and Lisa working together
= 20 × 25 × 30/20 × 25 + 20 × 30 + 25 × 30 days
= 15000/500 + 600 + 750 days
= 15000/1850 days
= 15000/1850 days
= 15000 ÷ 50/1850 ÷ 50 = 300/37 days
= 8 4/37 days or 8.108
Thus, Jessica, Karen, and Lisa together will finish the work in 8 4/37 days or 8.108 days Answer
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