# If three times the larger of the two numbers is divided by the smaller one, we get 4 as quotient and 3 as the remainder. Also, if seven times the smaller number is divided by the larger one, we get 5 as quotient and 1 as remainder. Find the numbers.

let the larger number be x and the smaller number be y.

3 times of the larger number = 3x

As dividend = divisor * quotient + remainder

since if the three times of the larger number is divided by the smaller number,

quotient = 4 and remainder = 3

if 7 times the smaller number is divided by the larger one , quotient =5 and remainder =1

multiply (1) by 5 and (2) by 3 and adding,

substtitue y=18 in (1):

thus the numbers are 18 and 25.

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