Question

A can do a work in 15 days and B can do it 30 days.In how many days will A and B together complete the work ?

Answer 1

work done by 'A' in 15 days = 1 work
so, work done by 'A' in 1 day = 1/15 part of a work
And,
     work done by'B' in 30 days = 1 work
so, ,work done by 'B' in 1 day = 1/30 part of a work
there work done by (A+B) in 1 day = 1/15+1/30 = 1/10 part of a work.
     1/10 part of a work done by (A+B) in 1 day
so, 1 work done by (A+B) in $\frac{1}{ \frac{1}{10} }$ days = 10 days

Answer 2

A can do a work in= 15 days
B can do a work in= 30 days
A's one day work rate= 1/15
B's one day work rate=1/30
To get their work rates combined, we'll add them=
 1   +   1     =   2 + 1     =   3     =   1  
15      30           30            30        10
To get the no. of days we do the reciprocal.
So the ans is 10 days.
:)