I have a brother 3 years elder to me. My sister was six years when my brother was born. The average of our ages is 14. How old is my sister now?

Correct option is A

Given:

Let my age be denoted as ( x ).
My brother is 3 years older than me, so his age is ( x + 3 ).
My sister was 6 years old when my brother was born. This means the difference between my sister's age and my brother's age is 6 years. So, my sister's age is ( x + 3 + 6 = x + 9 ).
Solution:

The average of our ages is 14, and the formula for average is given by:
$$Average = \frac{x + (x + 3) + (x + 9)}{3}$$​

We are given that the average of our ages is 14, so:
​$$14 = \frac{x + (x + 3) + (x + 9)}{3}$$​​
​$$14 = \frac{3x + 12}{3}$$​​
42 = 3x + 12
3x = 42 - 12
x = 10
So, my age is 10 years. Therefore, my sister's age is:
Sister's age = x + 9 = 10 + 9 = 19 years
My sister is 19 years old now.