Direct and Inverse proportion - how to understand approach to be taken The question is : 3 friends use 54 kg wheat for one month and then new friends came to join and consumed same amount of wheat in 18 days - so how many friends joined? Now if I look at this problem I can evaluate that less friends less wheat and more friends more wheat so direct proportion But then if we consider this way - more friends less days for same wheat and less friends more days for same wheat so inverse proportion Solving the problem using inverse proportion gives the correct answer 2 - that is 2 more friends joined. But how do we understand the concept here whether to use direct or in-direct proportion?

The intuitive distinction between the direct proportional equation $y=kx$ and the inverse proportion $xy=k$ is whether the variables rise and fall in the same direction.

In your problem, the number of people increased and the length of time their (fixed) food supply lasted decreased. (The 54 kg of food stayed the same in the problem and is therefore not a variable -- actually, the precise number is irrelevant.) That is what indicates an inverse proportional function like $3\times30=k=(3+x)\times18$.