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A can do a piece of work in 10 days, B in 12 days, and C in 15 days. All begin together but A leaves the work after 2 days and B leaves 3 days before the work is finished. How long did the work last?
By BYJU'S Exam Prep
Updated on: September 25th, 2023
The work lasts for 7 days. Steps to calculate the Duration of work last. From the given data we can write as:
- One day work of A = 1/10
- One day work of B = 1/12
- One day work of C = 1/15
Now by adding their work we get their one day’s work that is:
One day work of A, B, and C = 1/10 + 1/12 + 1/15
Taking lcm and simplifying we get:
As LCM of 5, 12, and 15 is 60
= (6 + 5 + 4)/60
= 15/60
= ¼
Consider the work to be completed in x days:
2 days work of A + (x – 3) days work of B + x days work of C = 1
2 x 1/10 + (x – 3) x 1/12 + x x 1/15 = 1
⅕ + (x – 3)12 + x/15 = 1
(12 + 5x – 15 + 4x)/60 = 60
As LCM of 5, 12, and 15 is 60
9x = 60 – 12 + 15
In simplification we get:
9x = 63
x = 7
Summary:
A can do a piece of work in 10 days, B in 12 days, and C in 15 days. All begin together but A leaves the work after 2 days and B leaves 3 days before the work is finished. How long did the work last?
A can do a piece of work in 10 days, B in 12 days, and C in 15 days. All begin together but A leaves the work after 2 days and B leaves 3 days before the work is finished. The work lasts for 7 days.
