If 2 is added to each of two given numbers,their ratio becomes 1:2.However,if 4 is subtracted from each of the given numbers,the ratio becomes 5:11.Find the numbers.

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Solution

Let the two numbers be x and y.

Case 1:

According to the given condition,

⇒ $\frac{x + 2}{y + 2} = \frac{1}{2}$

⇒ $2 x + 4 = y + 2$

⇒ $2 x - y = - 2$ .... (1)

Case 2:

Again, according to the given condition,

⇒ $\frac{x - 4}{y - 4} = \frac{5}{11}$

⇒ $11 x - 44 = 5 y - 20$

⇒ $11 x - 5 y = 24$ .... (2)

Now multiply equation (1) by subtract it from (2), we get

⇒ $11 x - 5 y - (10 x - 5 y) = 24 - (- 10)$

⇒ $11 x - 5 y - 10 x + 5 y = 24 + 10$

⇒ $x = 34$

On putting the value of x in (1), we get

$2 (34) - y = - 2$

⇒ $- y = - 2 - 68$

⇒ $y = 70$

Answer= 34 and 70

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