Two angles are in the ratio 1:2.on increasing the smaller angle by 6degree, and decreasing the larger angle by 6 degree, the ratio changed to2:3.what were the original angles?

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Solution

Let x and y be the angles.
given that
x:y=1:2
Ie
x/y =1/2
Or, y= 2x

Now consider the next hint:
Ie
Increasing the smaller angle by 6 and decreasing the larger by 6
Ie
x is the smaller angle.
So,
(x+6):(y-6) = 2:3
ie,
(x+6)/(y-6) = 2/3
Ie, on cross multipling,
3x+18= 2y-12
3x-2y = -30
We know that y=2x
Substitute this in equation.

3x - 2(2x) = -30

3x-4x = -30
-x= -30
Or angle x =30°
And angle y=2x =2×30= 60°

Hope you cleared the doubt.

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