Question

a and b can do a piece of work in 10 days b and c in 15days c and a in 18 days in how many days can be alone do it.

Answer 1

let a,b and c can do 1/A,1/B and 1/C of the work in each day 

$\frac{1}{A} + \frac{1}{B} = \frac{1}{10}$....(1)
$\frac{1}{B} + \frac{1}{C} = \frac{1}{15}$......(2)
$\frac{1}{A} + \frac{1}{C} = \frac{1}{18}$.......(3)
subtract (1) and (2)
$\frac{1}{A} - \frac{1}{C} = \frac{1}{10}- \frac{1}{15}=\frac{1}{30}$.....(4)
 add (4) and (3)
$\frac{2}{A} = \frac{4}{45}$
so A can do it 22.5 days
similarly B can do it 18 days
and C can do it  90 days