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The sum of the numerator and denominator of a fraction is 11. If the numerator is decreased by 1, the fraction becomes 14\frac{1}{4}41​​. Find the fra
Question

The sum of the numerator and denominator of a fraction is 11. If the numerator is decreased by 1, the fraction becomes 14\frac{1}{4}​. Find the fraction.

A.

38\frac{3}{8}​​

B.

29\frac{2}{9}​​

C.

47\frac{4}{7}​​

D.

56\frac{5}{6}​​

Correct option is A

Given:
Sum of numerator and denominator = 11
If numerator is decreased by 1, the fraction becomes 14\frac 14
Solution:
Let numerator = x => Denominator = 11 - x
Given:
x111x=144(x1)=1(11x)4x4=11x4x+x=11+4=>5x=15=>x=3\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 = 38\frac 38

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