# What will be the Sum of Numerator and Denominator of the Fration? If

If 1 is added to a denominator of a fraction, the fraction becomes 1/2. If 1 is added to the numerator, the fraction becomes 1. The sum of numerator and denominator of the fraction is

- 11
- 14
- 21
- 5

**Answer: (4) 5**

**Explanation:-
**Let the fraction be X/Y.

If 1 added to denominator,

Then, X/(Y + 1) = 1/2

2 X = Y + 1

2 X – Y = 1 ……………………….. (1)

If 1 added to numerator,

Then, (X + 1)/Y = 1

X + 1 = Y

X – Y = – 1 ………………………. (2)

Equation (2) subtracted from (1),

2 X – Y – X + Y = 1 + 1

X = 2,

Put the value of X = 2 in equation (1),

2 x 2 – Y = 1

4 – Y = 1

– Y = 1 – 4

Y = 3

Then, the fraction is X/Y = 2/3

Then, the sum of numerator an denominator = 2 + 3 = 5.

Hence, the answer is (4) 5.