Question

If the larger of two numbers is divided by the smaller, the quotient is 7 and the remainder is 6. But if 3 times the greater is divided by twice the smaller, the quotient is 11 and the remainder is 6. What are the numbers?

Answer 1

The numbers are `90 and 12`

Explanation:

Let the larger number be `x` and smaller number be `y`

By given conditions `x = 7 y+6 ; (1) , 3 x = 11*2 y+6 ; (2)`

`x = 7 y+6 ; (1) , 3 x = 22 y+6 ; (2)` Multiplying equation(1)

by `3` we get `3 x = 21 y+ 18 ; (3)` Subtracting equation(3)

from equation(2) we get `y-12=0 or y =12`. Putting `y=12`

in equation(1) we get `x = 7*12+6 or x =90` . Therefore,

the numbers are `90 and 12` [Ans]