Question

If 45 is subtracted from twice the greater of two numbers,it results in the other number.If 21 is subtracted from twice the smaller number,it results in the greater number.Find the numbers.

Answer 1

let x be greater number and y be the smaller number.
as per the question,

1st equation- $2x-45=y$

2nd equation -$x=2y-21$
⇒$x+\frac{21}{2}=y$

substituting the value of y in equation 1, we get
$2x-45=(x+\frac{21}{2}$
⇒ $2(2x-45)=x+21$
⇒ $4x-x=21+90$
⇒ $x=\frac{111}{3}$
∴ $x=37$

So, greater no. is 37.
on putting value of x in equation one we get,
$2x-45=y$
$2\times 37-45=y$
⇒ $74-45=y$
∴ $y=29$

so, the value of greater no. and smaller no. respectively are:- 37 and 29 respectively