List<Detail_Type__c> allDetails = [
 SELECT Id
 FROM Detail_Type__c
 WHERE Master_Type__c = :Id
];
Integer res = allDetails.size();

List<Master_Type__c> allDetails = [
 SELECT Master_Type_Field1__c, Master_Type_Field2__c, (SELECT NumberOf Detail_Type__r)
 FROM Detail_Type__c
 WHERE Master_Type_FieldDoesNotMatter_c = :something
];

List<AggregateResult> result = [
    select count(Id)cnt, Master_Type__c
    from Detail_Type__c
    where Master_Type__c in :masterIds
    group by Master_Type__c
    ];

for (AggregateResult ar : result)  {
    System.debug('Master_Type__c' + ar.get('Master_Type__c'));
    System.debug('Count' + ar.get('cnt'));
}