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The basis definition of contigencies is the expected cost / expenses / loss; which did not materlies at the time of issuance of financial statement..
Generally companies maintain the petty cash for small amount of contingencies. The certain amount of contigencies could be created under the outstanding expenses in the books of account to meet contigencies.
While the contingent liabilities are unconfirmed loss or receoveries. which are reflected at the bottom of balance sheet with proper explanation in the notes to FS. such as a law suit against the firm.