Rakesh, a 7–year old boy had itchy, excoriated papules on the forehead and the exposed parts of the arms and legs for 3 years. The disease was most severe in the rainy season and improved completely in winter. Most likely diagnosis is
Some guides have given atopic dermatitis and I would like to exclude this option first: ­

Exclusion of atopic dermatitis

This child is presenting at the age of 7 years with a history of disease starting 3 years back → that means the disease was started at 4 years of age.
There is involvement of the forehead (face) and exposed part of arms and legs.
You can easily exclude atopic dermatitis:- In childhood atopic dermatitis neither face is involved nor exposed part of extrimities.

There is involvement of flexures (and sometime extensor surfaces).
Exclusion of urticaria

Urticaria presents as itchy mythmatous lesions which are transient.
Lesions are usually not excoriated (as given in question) patients tend to rub rather than scratch their lesions.
Further, there are many types of urtacaria (e.g. cholinergic, cold etc), but no one is improved in winter, (rather cold urticaria is precipitated by cold weather).

Eclusion of scabies

In scabies burrows are a very important feature (not present in this child).
Areas involved are :- Fingers, web spaces, palms wrist, points of elbow, the buttocks, the abdomen, anterior axillary fold, the legs and feet.
Usually, there is a history of exposure or multiple cases in the family.

Now we are left with insect bite hypersensitivity; you can go ahead simply by the exclusion of other 3 options. If you still require some explanation, read below:-
Insect bite hypersensitivity

In this question, the lesions are on a face (forehead) and other exposed part of extremities → you know insect bite is on exposed parts.
Lesions are most severe in rainy season → Rainy season is the period when there are maximum numbers of insects."Insect bites, fungal infections and bacterial infections are aggravated in the summer/rainy season".
Lesions improved in winter → most of the insects disappear during winter.
So, this child is most likely suffering from localized (lesions are on the sites of bite, i.e. exposed area) due to a repeated bite of the insect.
Insect bite hypersensitivity
Scabies
Urticaria
Atopic dermatitis