# Q. Which one of the following will have minimum change in its value if s is added to both numerator and the denominator of the fractions 2/3, 3/4, 4/5 and 5/6?

(a) 2/3

(b) 3/4

(c) 4/5

(d) 5/6

Correct Answer: (d) 5/6

#### Question from UPSC Prelims 2020 CSAT Paper

**Explanation : **

## S is added to both numerator and the denominator

Let’s say we add s to both the numerator and denominator of each fraction. The new fractions would be:

(2 + s)/(3 + s)

(3 + s)/(4 + s)

(4 + s)/(5 + s)

(5 + s)/(6 + s)

The change in value for each fraction would be the difference between the new and old fractions:

|(2/3) – ((2 + s)/(3 + s))|

|(3/4) – ((3 + s)/(4 + s))|

|(4/5) – ((4 + s)/(5 + s))|

|(5/6) – ((5 + s)/(6 + s))|

To find which fraction has the minimum change in value, we can compare these expressions. However, since s is unknown and could be positive or negative, it’s difficult to directly compare them.

Instead, let’s consider what happens when s is very large. In that case, the terms 2, 3, 4, and 5 in the numerators become negligible compared to s. Similarly, the terms 3, 4, 5, and 6 in the denominators become negligible compared to s. So when s is very large, all four fractions are approximately equal to 1.

In other words, as we add larger and larger values of s to both numerator and denominator of each fraction, all four fractions get closer and closer to 1. Since 5/6 is already closest to 1 among all four fractions, it will have the minimum change in its value.