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) = 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.