Question

from each of two given numbers, half the smaller number is subtracted. of the resulting numbers the larger one is three times as large as the smaller. what is the ratio of the two numbers ?

Answer 1

if nos are x and y, then 

(x-y/2)/(y/2)=3
x=2y
x/y = 2/1

2:1
let smaller no. be x and larger no. b y
acc. to given condition
3(x-x/2)=(y-x/2)
=>4x=2y
=>y/x=2:1

Answer 2

Given: From each of two given numbers, half the smaller number is subtracted. Of the resulting numbers, the larger one is three times as large as the smaller.

To find: The ratio of two numbers

Let: The smaller number be $x$ and larger number be $y$

Solution:

According to the given question and assumption made,

Half of the smaller number will be $\frac{x}{2}$ and after subtracting half of smaller number from each of the given numbers, the numbers will be

∵ $x \ - \ \frac{x}{2} \ and \ y \ - \ \frac{x}{2}$

Since same value has been subtracted from both the numbers, the larger number is $y \ - \ \frac{x}{2}$.

Now, $y \ - \ \frac{x}{2} = 3( x \ - \ \frac{x}{2})$

⇒ $y \ - \ \frac{x}{2} = 3x \ - \ \frac{3x}{2}$

⇒ $y = 3x - \frac{3x}{2} + \frac{x}{2}$

⇒ $y = \frac{6x \ - \ 3x \ + \ x}{2} = \frac{4x}{2} = 2x$

⇒ $\frac{y}{x} = \frac{2}{1}$

i.e., $x : y = 1:2$

Hence, the ratio of the two numbers is 1 : 2.