Two angles are in the ratio `1: 2`. On increasing the smaller angle by `6^(circ)` and decreasing the larger angle by `6^(circ)`, the ratio changed to `2: 3 .` What were the original angles?

Explanation

Angles be `x` and `2 x`
`(x+6^(circ)):(2 x-6)^(circ)=2 x: 3 x`
That is, `2 x(2 x-6)=3 x(x+6)`
`4 x^2-12 x=3 x^2+18 x`
`x^2-30 x=0`
`x(x-30)=0 ` ie `x=30`
`therefore` Original angles `30^(circ), 60^(circ)`