Discussion

Explanation:

Here, only 5/4 and 3/2 are greater than 1. So, let’s consider only these two ratios. Other 2 ratios are smaller than 1.

To find the greatest ratio, we must bring each of the ratio to common denominator.

Thus, $\frac{5}{4}, \frac{3}{2}$ ≡$\frac{5}{4}, \frac{3}{2}\times \frac{2}{2}$ ≡ $\frac{5}{4}, \frac{6}{4}$ 

Hence, ratio 3 : 2 is the greatest ratio.

Hence, option (b).

Alternately,

If a/b > 1, ⇒ $\frac{a+x}{b+x}<\frac{a}{b}$

Hence, $\frac{5}{4}$ = $\frac{3+2}{2+2}$ < $\frac{3}{2}$.

Alternately,

Assume $\frac{5}{4}>\frac{3}{2}$

⇒ 5 × 2 > 3 × 4

⇒ 10 > 12, which is not true. 

Hence our assumption was wrong.

∴ 3/2 is the greatest ratio.

Hence, option (b).

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