Question

If three times the greater of 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 greater one, we get 5 as the quotient and 1 as the remainder. Find the numbers. 

Answer 1

Let the greater no. be x and smaller no. be y

Given, 3x = 4y + 3     ...(i)

By using:

Dividend = Divisor × Quotient + Remainder. 

7y = 5x + 1        ...(ii)

Multiply by eqn (i) by 5 and (ii) by 3 

15x − 20y = 15         ...(iii)

−15x + 21y = 3         ...(iv)

On adding y = 18

from equation (i) 

`x = (18 xx 4 + 3)/3`

= `75/3`

= 25

Greater number = 25

Smallest number = 18