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let the numbers be 6x and 5x
sum of the numbers is 6x+5x = 11x
11x = 77 therefore x = 7
difference of the numbers is $$6x - 5x $$ = x = 7
alternatively
ratio of two numbers given is 6:5
sum of the numbers is 6+5 = 11 units
now 11 units is 77
1 unit = 7
difference between the numbers is $$6-5$$ = 1unit = 7
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