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Difference between Run out at something and Run out on something

run out at something—(also: run up to something ) amount to a figure mentioned; reach a sum:

  • With hospitals making about 50 million outpatients’ appointments a year, the annual cost of missed appointments runs out at more than £300 million.

run out on somethingabandon one’s responsibility for smth.; fail to fulfil an agreement, etc.:

  • We should not have a situation where people can run out on their obligations to others.