One of the most important and conceptual question from linear equations in two variables in which we have to find the numbers if 2 is added to each one of the two given number,then their ratio becomes 1:2 However if 4 is subtracted from each of the given number,the ratio becomes 5:11.

RS Aggarwal, Class 10, Chapter 3E, question no 9

Let the required numbers be x and y.

Now, we have: x+2/ y+2 = 1/2

By cross multiplication, we get:

2x + 4 = y + 2

⇒ 2x – y = -2 ……(i)

Again, we have:

x−4/ y−4 = 5/11

By cross multiplication, we get:

11x – 44 = 5y – 20

⇒11x – 5y = 24 ……(ii)

On multiplying (i) by 5,

we get:

10x – 5y = -10

On subtracting (iii) from (ii),

we get:

x = (24 + 10) = 34

On substituting x = 34 in (i),

we get: 2 × 34 – y = -2

⇒ 68 – y = -2

⇒ y = (68 + 2) = 70

Hence, the required numbers are 34 and 70.