Question

If three times the larger of two numbers is divided by the smaller number the quotient is 6 and the remainder is 6. If 5 times the smaller number is divided by the larger number the quotient is 2 and the remainder is 3. Find the numbers

Answer 1

let the larger number be x and smaller number be y . then
equation 1 
3x/y = 6
⇒ 3x = 6y 
⇒3x - 6y = 0 ....................i

equation 2 
5y/x = 2 
⇒5y = 2x
⇒2x - 5y = 0 ......................ii

eq i × 2 and eq ii × 3
 6x - 12y = 0 .........................iii
6x - 15y = 0...........................iv

subtracting eq iv from iii
we get
3y= 0 
⇒y= 0
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