Question

If three times the larger 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 the quotient and 1 as the remainder. Find the numbers.

Answer 1

Answer :

Let the larger number = x

Let the smaller number = y


So, from first condition we get

3x = 4y + 3

3x - 4y = 3 ------------------------ ( 1 )

And

from Second condition we get

7y = 5x + 1

5x - 7y = - 1 ------------------------ ( 2 )

Now we multiply by 5 in equation 1 and by 3 in equation 2 , And get

15x - 20y = 15 ------------------------ ( 3 )

And

15x - 21y = - 3 ------------------------ ( 4 )

Now we subtract equation 4 from equation 3 and get

y = 18 , Substitute that value in equation 1 and get


3x - 4( 18 ) = 3

3x - 72 = 3

3x = 75

x = 25

So,

larger number = x = 25

smaller number = y = 18