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?

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.