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in Linear Equations by (34.1k points)
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The denominator of a fraction is 4 more than twice its numerator. Denominator becomes 12 times the numerator, if both the numerator and the denominator are reduced by 6. Find the fraction.

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Let the numerator of the fraction be x and the denominator be y.

\(\therefore\) Fraction = x/y

According to the first condition,

y = 2x + 4 

∴ 2x – y = -4 …(i)

According to the second condition,

(y – 6)= 12(x – 6) 

∴ y – 6 = 12x – 72 

∴ 12x – y = 72 – 6 

∴ 12x – y = 66 …(ii)

Subtracting equation (i) from (ii), we get

Substituting x = 7 in equation (i), we get

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