Please help me with these accounting questions

1. How can a business entity have controlling interest of another business entity when it does not own over 50% of the parent company ordinary share capital?
2. Why are inventories excluded when calculating the Acid test ratio under “Liquidity ratios"?
3. Why are the intra-group profits eliminated during consolidation? Explain with an example
4. Provide one reason on why the amount paid for a business (during takeover) may differ from that of the balance sheet value of its net assets?