If three times the larger number of the two numbers is divided by the smaller one,we get 4 as the 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 the remainderr,find the numbers.

Let the larger number be x and smaller number be y 

Hence, 3x  = 4y+3 (1)

7y = 5x + 1 (2)

 

Multiplying equation (1) by 5 and equation(2) by 3

15x = 20y + 15

21y = 15x + 3

Adding

21y = 20y + 18

y = 18

 

3x = 4(18) + 3 = 75

x = 25

 

Hence, the 2 numbers are 18 and 25.