Question

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.

Answer 1

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)

x = 34

On substituting x = 34 in (i), we get:

2 × 34 – y = –2

⇒ 68 – y = –2

⇒ y = (68 + 2)

⇒ y = 70

Hence, the required numbers are 34 and 70.