**Ques -** **The ratio of numerator to a denominator of a fraction is 1/5 when x and 5x are added to the numerator and denominator respectively to the given fraction then the ratio of the new fraction will be :**

**(a) 1 : 1**

**(b) 1 : 25**

**(c) 1 : 5**

**(d) 2 : 7**

**Solution - **

Let,

The ratio of numerator to a denominator of a fraction is 1/5.

The numerator = k

The denominator = 5k

when x and 5x are added to the numerator and denominator.

Then,

The numerator = k + x

The denominator = 5k + 5x

= (k + x) / (5k + 5x)

= (k + x) / 5(k + x)

= 1/5

**= 1 : 5 **

Thus,

**The ratio of the new fraction will be 1 : 5.**

Hence,

The correct answer is option **(c) 1 : 5.**

Thank You