The sum of the numerator and denominator of a fraction is 11. If the numerator is decreased by 1, the fraction becomes $$\frac{1}{4}$$​. Find the fraction.

Correct option is A

Given:
Sum of numerator and denominator = 11
If numerator is decreased by 1, the fraction becomes $$\frac 14$$​
Solution:
Let numerator = x => Denominator = 11 - x
Given:
​$$\frac{x - 1}{11 - x} = \frac{1}{4} \\4(x - 1) = 1(11 - x) \\4x - 4 = 11 - x \\4x + x = 11 + 4 \Rightarrow 5x = 15 \Rightarrow x = 3$$​​
Numerator = x = 3
Denominator = 11 - x = 8
Fraction = $$\frac 38$$​