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.