Question

The denominator of a fraction is 4 less than twice the numerator.if both numerator and denominator are decreased by 6 ,then denominator becomes twelve times the numerator. What is the fraction?

Answer 1

• Let Numerator be N

and

• Denominator be D.

Fraction = $\dfrac{N}{D}$

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» The Denominator of a fraction is 4 less than twice the Numerator.

=> D = 2N + 4 _______ ( eq 1)

» And Denominator are decreased by 6 then, Denomination becomes twelve times the Numerator.

=> D - 6 = 12(N - 6)

=> D - 6 = 12N - 72

=> (2N + 4) - 6 = 12N - 72 [From (eq 1)]

=> 2N - 2 = 12N - 72

=> 2N - 12N = - 72 + 2

=> - 10N = - 70

=> 10N = 70

=> N = 7

• Put value of N in (eq 1)

=> D = 2(7) + 4

=> D = 14 + 4

=> D = 18

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Fraction = $\dfrac{N}{D}\:=\:\dfrac{7}{18}$

________ [ ANSWER ]

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✡ Verification :

We have equation D = 2N + 4 (according to Question)

From above calculations we have D = 18 and N = 7

Put them in above equation

→ 18 = 2(7) + 4

→ 18 = 18

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Answer 2

Step-by-step explanation:

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