Why inter company transactions are eliminated in consolidation?

to apply the single entity concept 

as the receivable and payable will be doubled if they added together 

During consolidation process,inter company transactions must be eliminated to reflect real picture of group financial statements.If they are not elimminated, the receivable,payables and inventory in balance sheet and profit in the income statement will be misstated.

When you prepare Consolidated Financial Statements, you wish them to show the financial postion of the Group as a whole. Now, a payable, receivable would have a Zero net effect Overall but it would over state the receivable or payables of the group as whole if inter company balances were recognized.So they are eliminated upon Consolidation.Mind you, they still remain in the individual accounts.