Total hours of television watched: 60 x 0.5 = 30 hours

SO, when we evaluate the ratios, the need to be 'compatible' with a total of 30 hours. It means that we should be able to find integers N & R such as N x 2 + R x 1.5 = 30

1) 3 x 2 / 16 x 1.5 = 6/24 --> Compatible (N=3, R=16)

2) 1 x 2 / 2 x 1.5 = 2/3 = 12/18 --> Compatible (N=6, R=12)

3) 2 x 2 / 3 x 1.5 = 4/4.5 --> Not compatible

4) 9 x 2 / 8 x 1.5 = 18/12 --> Compatible (N=9, R=8 )

5) 3x2 / 1x1.5 = 6/1.5 = 24/6 --> Compatible (N=12, R=4)

Let me know if unclear

From the question we know

2n + 1.5r = 30

OR 4n+3r=60

lets say n/r = x --> this is what we need to find

n = rx (substitute for n in the eq above)

4rx+3r=60

r(4x+3)=60

Now plug in all the answer choices for x and find out choice for which r is not an integer

x=3/16 gives r=16
x=1/2 gives r=12
x=2/3 gives r=180/11 ---> this is your answer