Question:
Carolyn can finish a work in 96 days. Catherine can finish the same work in 101 days while Maria can finish the work in 106 days. How long will it take to finish it if they work together?
Correct Answer
33 9351/15289 days or 33.612 days
Solution And Explanation
Solution
Given,
The number of days required to finish a piece of work by Carolyn = 96 days
And, the number of days required to finish the same work by Catherine = 101 days
And, the number of days required to finish the same work by Maria = 106 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 96 days the work is done by Carolyn = 1
∴ The work done by Carolyn in 1 day = 1/96
Similarly,
∵ In 101 days the work is done by Catherine = 1
∴ The work done by Catherine in 1 day = 1/101
Similarly,
∵ In 106 days the work is done by Maria = 1
∴ The work done by Maria in 1 day = 1/106 part
Now, the work done by Carolyn, Catherine, and Maria together in 1 day
= Carolyn's 1 day work + Catherine's 1 day work + Maria's 1 day work
= 1/96 + 1/101 + 1/106
= 5353 + 5088 + 4848/513888
= 15289/513888 part of work
This means in 1 day, 15289/513888 part of work is done by Carolyn, Catherine and Maria working together.
Now, the number of days required to finish 15289/513888 part of work by Carolyn, Catherine, and Maria working together = 1
∴ the number of days required to finish the whole work (1 work) by Carolyn + Catherine + Maria together
= 1/15289/513888
= 1 × 513888/15289 = 513888/15289 days
= 33 9351/15289 days = or 33.612 days
Thus, Carolyn, Catherine, and Maria working together will finish the total work (1 work) in 33 9351/15289 days = or 33.612 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 Carolyn = 96 days
And the number of days required to finish the same work by Catherine = 101 days
And the number of days required to finish the work by Maria = 106 days
Thus, the number of days required to finish the work by Carolyn, Catherine, and Maria together = ?
Here a = 96 days
And, b = 101 days
And, c = 106 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Carolyn, Catherine, and Maria working together
= 96 × 101 × 106/96 × 101 + 96 × 106 + 101 × 106 days
= 1027776/9696 + 10176 + 10706 days
= 1027776/30578 days
= 1027776/30578 days
= 1027776 ÷ 2/30578 ÷ 2 = 513888/15289 days
= 33 9351/15289 days or 33.612
Thus, Carolyn, Catherine, and Maria together will finish the work in 33 9351/15289 days or 33.612 days Answer
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