Question

a and b together finishes the work in 12 days if a alone can finish the same work in 20 days .how many days b alone can do

Answer 1

a+b's work in 1 day = 1/12
a's work in 1 day = 1/20
b's work in 1 day = 1/x
so
a's work+b's work = a+b's work
1/20+1/x=1/12
12(x+20)= 20x
12x + 240 = 20x
20x - 12x = 240
8x = 240
x = 30
so a's work along takes 30 days 

Answer 2

Let the amount of work be x

Time required for a to complete the x amount of work = a days
Work done by a
= x/a
= (x/20)

Time required for b to complete the same amount of work = 'b' days
Work done
= x/b

Time required for a and b to complete the work together = 12 days
Total work done by a and b

= (x/a)+(x/b) = (x/12)
(x/20) + (x/b) = (x/12)
(20+b)x/20b = x/12
(240+12b) x = 20b x
240 = 8b
b = 30
===========================
Hence b can alone do the work in 30 days