Question

Two numbers are in the ratio 4:5. If 30 is subtracted from each of the numbers, the ratio becomes 1:2. Find the numbers.

Answer 1

Let the common multiple between the numbers be x.
So, the numbers are x & y

`x/y = 4/5`    ...(i)

`(x - 30)/(y - 30) = 1/2`

2(x - 30) = y - 30

2x - 60 = y - 30

2x - y = 30    ...(ii)

From eq. (i) & (ii )

`2 (4/(5y)) - y = 30`

`(8y)/5 - y  =30`

`(8y-5y)/5 =30`

3y = 150

`y = 150/3` 

y = 50

from eq. (ii)

`x = 4/5(50)`

x = 4 × 10

x= 40