Question

A can complete a work in 10 days, B in 12 days and C in 15 days. all of them began the work together, but A had to leave the work after 2 days of the start and B, 3 days before the completion of the work. How long did the work last?​

Answer 1

$\huge \cal \underline \color{magenta}★A᭄ɴsᴡΣʀ࿐$

First 2 days all three of them worked together, thus they did 2*(1/10 + 1/12 + 1/15) = 1/2 of the work.

Last 3 days only Carla worked, thus she did 3/15 = 1/5 of the work.

1 - 1/2 - 1/5 = 3/10 of the work was done by Ben and Carla:

(time)*(combined rate)=(job done)

⇢ t*(1/12 + 1/15) = 3/10

⇢t = 2 days.

So, we have that Ben and Carla worked together for 2 days.

Total days = 2 + 3 + 2

ᴀɴsᴡᴇʀ = 7

Answer 2

Answer:

$\huge\mathtt{\red{\underline{\underline{Answer}}}}$

First 2 days all three of them worked together, thus they did 2*(1/10 + 1/12 + 1/15) = 1/2 of the work.

Last 3 days only Carla worked, thus she did 3/15 = 1/5 of the work.

1 - 1/2 - 1/5 = 3/10 of the work was done by Ben and Carla:

(time)*(combined rate)=(job done)

⇢ t*(1/12 + 1/15) = 3/10

⇢t = 2 days.

So, we have that Ben and Carla worked together for 2 days.

Total days = 2 + 3 + 2

ᴀɴsᴡᴇʀ = 7