HI Rohit,
You can use below code to get started

trigger AccountBudgetDistribution on Account (after update) {
    List<Account> updatedAccounts = new List<Account>();
    List<Contact> salesContacts = new List<Contact>();
    List<Contact> marketingContacts = new List<Contact>();
    for(Account acc: Trigger.new){
        Account oldAcc = Trigger.oldMap.get(acc.Id);
        if(acc.Budget__c != oldAcc.Budget__c){
            updatedAccounts.add(acc);
        }
    }
    if(updatedAccounts.size()>0){
        for(Account acc: updatedAccounts){
            //Dividing budget into two portions
            Decimal salesBudget = 0;
            Decimal marketingBudget = 0;
            if(acc.Budget__c!=null && acc.Budget__c!=0){
                salesBudget = acc.Budget__c * 0.6;
                marketingBudget = acc.Budget__c * 0.4;
            }
            //Getting all contacts that have Use Sales Budget checkbox checked
            salesContacts = [SELECT Id, Use_Sales_Budget__c FROM Contact WHERE AccountId = :acc.Id AND Use_Sales_Budget__c = true];
            if(salesContacts.size()>0){
                //Calculating Sales budget per Contact
                Decimal salesBudgetPerContact = salesBudget/salesContacts.size();
                //Updating the budget for each Contact
                for(Contact con: salesContacts){
                    con.Budget__c = salesBudgetPerContact;
                }
            }
            //Getting all contacts that have Use Marketing Budget checkbox checked
            marketingContacts = [SELECT Id, Use_Marketing_Budget__c FROM Contact WHERE AccountId = :acc.Id AND Use_Marketing_Budget__c = true];
            if(marketingContacts.size()>0){
                //Calculating Marketing budget per Contact
                Decimal marketingBudgetPerContact = marketingBudget/marketingContacts.size();
                //Updating the budget for each Contact
                for(Contact con: marketingContacts){
                    con.Budget__c = marketingBudgetPerContact;
                }
            }
        }
        //Updating Contacts with new budget values
        if(salesContacts.size()>0 || marketingContacts.size()>0){
            update salesContacts;
            update marketingContacts;
        }
    }
}

This trigger on Account that divides the budget into two portions (60% for Sales and 40% for Marketing), and then equally distributes each portion among the Contacts of that Account that have the appropriate checkbox checked.

I have created custom fields Budget__c(number), Use_Marketing_Budget__c(checkbox),Use_Sales_Budget__c(checkbox) on contact object that are used in this code

If this information helps, please mark the answer as best. Thank you