Question : Angela can finish a work in 70 days. Anna can finish the same work in 75 days while Brenda can finish the work in 80 days. How long will it take to finish it if they work together?
Correct Answer 24 312/337 days or 24.926 days
Solution & Explanation
Solution
Given,
The number of days required to finish a piece of work by Angela = 70 days
And, the number of days required to finish the same work by Anna = 75 days
And, the number of days required to finish the same work by Brenda = 80 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 70 days the work is done by Angela = 1
∴ The work done by Angela in 1 day = 1/70
Similarly,
∵ In 75 days the work is done by Anna = 1
∴ The work done by Anna in 1 day = 1/75
Similarly,
∵ In 80 days the work is done by Brenda = 1
∴ The work done by Brenda in 1 day = 1/80 part
Now, the work done by Angela, Anna, and Brenda together in 1 day
= Angela's 1 day work + Anna's 1 day work + Brenda's 1 day work
= 1/70 + 1/75 + 1/80
= 120 + 112 + 105/8400
= 337/8400 part of work
This means in 1 day, 337/8400 part of work is done by Angela, Anna and Brenda working together.
Now, the number of days required to finish 337/8400 part of work by Angela, Anna, and Brenda working together = 1
∴ the number of days required to finish the whole work (1 work) by Angela + Anna + Brenda together
= 1/337/8400
= 1 × 8400/337 = 8400/337 days
= 24 312/337 days = or 24.926 days
Thus, Angela, Anna, and Brenda working together will finish the total work (1 work) in 24 312/337 days = or 24.926 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 Angela = 70 days
And the number of days required to finish the same work by Anna = 75 days
And the number of days required to finish the work by Brenda = 80 days
Thus, the number of days required to finish the work by Angela, Anna, and Brenda together = ?
Here a = 70 days
And, b = 75 days
And, c = 80 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Angela, Anna, and Brenda working together
= 70 × 75 × 80/70 × 75 + 70 × 80 + 75 × 80 days
= 420000/5250 + 5600 + 6000 days
= 420000/16850 days
= 420000/16850 days
= 420000 ÷ 50/16850 ÷ 50 = 8400/337 days
= 24 312/337 days or 24.926
Thus, Angela, Anna, and Brenda together will finish the work in 24 312/337 days or 24.926 days Answer
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