How to make total of products based on product category laravel

Guys iam working with a project Inventory Control like project.

I have a table product_category with columns

id(pk),
login_user_id,
product_category_name

ans this is my product table with columns

id(pk),
login_user_id,
product_name,
product_category_id,

and this is purchase_product table with columns

id(pk),
login_user_id,
date,
product_id,
qty,
total_amount

Now what my client expecting is i need to have the total amount based on the category of the product.

say for example.

if i have data in purchase_product table like

date        Product             qty     total_amount    
30-03       coconut oil         10      1000
30-03       ground nut oil      20      2000
30-03       Seasame oil         30      3000
30-03       Onion               10      200
30-03       tomato              20      200

in the above table first three belongs to oil type category. and second two belongs to vegetables category.

now how i need the total is

Oil - 6000

Vegetables -- 400

i need to get the total amount of the products based in its category.

here whats the problem is i didnt give product_category in the purchase_product table

but i have product_category table and product table with relationship.

How can i do this please Kindly help me for this.

i need to fetch based on date.

i have a date field in my blade file. i will choose the date and click the search button.

it moves to search_purchase_product method in controller there i need to search this date and the total amount with based on product category.

How to do this please Kindly help mee please.

I know the i need to use groupby

but whats my problem is in my purchase_product table i dont have product_category column

so what should i don please some one help.

and these are my models

ProductCategory

Product

PuchaseProduct

Kindly some one help please...