Question

If three times the larger of two numbers is divided by the smaller,we get 4 as the quotient and 8 as the remainder.If five times the smaller is divided by the larger,we get 3 as the quotient and 5 as the remainder.Find the numbers.

Answer 1

Let larger number be x

and smaller number be y

First condition

$Dividend=Divisor\times Quotient+Remainder$
$3x=y\times 4+8$
$3x=4y+8$
$3x-4y=8$
Second condition
$5y=3x+5$
$5y-3x=5$
$3x-4y=8$ .............1

$-3x+5y=5$.............2
Eliminate y
Multiply (1)by 5
Multiply (2) by 4
$15x-20y=40$
$-12x+20y=20$
Add the two equations
$3x=60$

$x=20$

put value of x in (1)
$3x-4y=8$
$60-4y=8$
$-4y=8-60$
$-4y=-52$
$y=\frac{-52}{-4}=13$
$x=20$
$y=13$