If the numerator and denominator of a ratio are increased by the same positive number, then the value of the ratio may increase / decrease or remain unchanged depending upon the value of the ratio. Let us take three different cases:

1. Suppose the ratio is \(\frac{1}{2}\), on increasing numerator and denominator by 1, we get another ratio \(\frac{2}{3}\), which is more than the initial value. 
2. Suppose the initial value of the ratio is \(\frac{3}{2}\), then on adding 1 on numerator and denominator it becomes \(\frac{4}{3}\) which is less than the initial value of the ratio. 
3. Suppose the initial value of the ratio is \(\frac{2}{2}\), then on increasing the numerator and denominator by the same value ratio remains unchanged.

Hence if a ratio is less than 1, then it increases on adding the same number to numerator and denominator and similarly if a ratio is more than 1, it decreases on adding the same number to numerator and denominator.

If \(\frac{a}{b}\) >1, then \(\frac{{a + x}}{{b + x}} < \frac{a}{b}\)

If \(\frac{a}{b}\) < 1, then \(\frac{{a + x}}{{b + x}} > \frac{a}{b}\)

Where  \(x\)  is a positive real number

Example: What is the biggest number out of the four given fractions\(\frac{{91}}{{97}},\frac{{93}}{{99}},\frac{{90}}{{96}},\frac{{92}}{{98}}\)?

Solution:  Since all the ratios are less than 1. Hence if we increase numerator and denominator by a constant value, ratio will increase.

\( \Rightarrow \frac{{93}}{{99}}\) is the biggest and \(\frac{{90}}{{96}}\) is the smallest.

Example: If the ratio of the present ages of Ram and Shyam is 4 : 3, which of the following cannot be the ratio of their ages 5 years from now?

(1) 1.34
(2) 1.35
(3) 1.36
(4) 1.37
(5) All of these

Solution: Since the ratio of the present ages is more than one. Hence after 5 years, ratio will decrease. Because if\(\frac{a}{b} > 1\), then \(\frac{{a + x}}{{b + x}} < \frac{a}{b}\), where \(x\) is a positive number.

Hence all the four ratios are not possible. Answer is choice (5)