Question

The average of two numbers is 62. if 2 is added to the smaller number the radio between the numbers becomes 1:2. the smaller number is

Answer 1

Hello,

Let the 2 numbers be x and y where x is smaller one.

The average of the two numbers is 62
So ,
$\frac{x + y}{2} = 62 \\ \\ x + y = 62 \times 2 = 124........(1)$
Now
Is
If 2 is added to smaller number then the number becomes x+2 and its ratio to the larger number becomes 1:2
So ,
$\frac{x + 2}{y} = \frac{1}{2} \\ \\ 2(x + 2) = y \\ 2x + 4 =y \\ 2 x - y = ( - 4)........(2)$
We have got two equations now
We will add the two equations
Now,
On adding we get :-

$x + y = 124 \\ 2x - y = - 4 \\ = = = = = = = = = \\ 3x = 120 \\ \\ x = \frac{120}{3} = 40$
Putting in second equation to get y
we get
$2x - y = - 4 \\ y = 2x + 4 \\ y = 2 \times 40 + 4 = 84$
So,

The smaller number is x that is equal to 40

Hope this will be helping you ✌️