Question

The denominator of a fraction is 4 more than twice the numerator. When both numerator and denominator are decresed by 6, then the denominator becomes 12 times the numerator. Find the fraction.​

Answer 1

Step-by-step explanation: Hope it helps you!

Answer 2

Given:

• The denominator of a fraction is 4 more than twice the numerator.

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To Find:

• Find the fraction.

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Solution:

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

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According to question,

• The denominator of a fraction is 4 more than twice the numerator

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$\leadsto \sf y = 2x + 4 \\ \\ \leadsto \sf 2x - y = 4 \: \: eq (i)$

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Now,

• When both numerator and denominator are decresed by 6, then the denominator becomes 12 times the numerator.

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$\leadsto \sf(y - 6) = 12(x - 6) \\ \\ \leadsto \sf y - 6 = 12x - 72 \\ \\ \leadsto \sf 12x - y = 72 - 6 \\ \\ \leadsto\sf 12x - y = 60 \: \: \: eq\: (ii)$

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Subtracting (i) from(ii)

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$\leadsto \sf 12x - 2x - y - (-y) = 66 - (- 4) \\ \\ \leadsto \sf12x -2x -y + y = 66 + 4 \\ \\ \leadsto \sf10x = 70 \\ \\ \leadsto \sf x = \frac{70}{10} \\ \\ \leadsto \sf x = 7$

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Substituting x in equation (ii)

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$\leadsto \sf 2x - y = 4 \\ \\ \leadsto \sf2 × 7 - y = 4 \\ \\ \leadsto \sf14 - y = 4 \\ \\ \leadsto \sf y = 14 + 4 \\ \\ \leadsto \sf y = 18$

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${ \underline{ \sf \therefore \red{ The \: required \: fraction \: is \: \dfrac{7}{18}}}}$

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