Question

10. The numerator of a fraction is 6 less than the denominator. If 1 is added to both the numerator and
the denominator, the fraction becomes 1/2. Find the fraction.
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Answer 1

Answer:

Let the denominator be x

then, numerator = x-6

according to question ,

=> (x-6)+3/x = 2/3

=> (x-6+3)/x = 2/3

=> (x-3)/x = 2/3

=> 3(x-3) = 2x

=> 3x-9 = 2x

=> 3x-2x = 9

=> x = 9. (denominator)

numerator = x-6 => 9-6 = 3

then , fraction = 3/9

Step-by-step explanation:

Answer 2

Let the denominator be x

So, the numerator is 6 less than the denominator. (Given)

∵ Numerator = (x - 6)

$\blue{\underline{\underline{\sf{According\:\:to\:\:question:}}}}$

If 1 is added to both the numerator and  the denominator, the fraction becomes 1/2. Find the fraction.

$\red{\implies \dfrac{(x-6)+1}{x+1} = \dfrac{1}{2}} \\ \\ \\ \red{\implies \dfrac{x-5}{x+1} = \dfrac{1}{2}} \\ \\ \\ \star [\sf cross\:\:multiplication]\\ \\ \\ \implies 2(x-5) = 1(x+1) \\ \\ \implies 2x - 10 = x + 1 \\ \\ \implies 2x - x = 1 + 10 \\ \\ \star [Taking\: x\:to\: LHS\:and\:(-10) \:to RHS ] \\ \\ \implies x = 11$

Hence

Denominator = x = 11

Numerator = (x-6) = 11 - 6 = 5

The original fraction

$= \boxed{\boxed{\red{\dfrac{5}{11}}}}$

Verification

$\dfrac{5+ \red{1} }{11+ \red{1} } = \dfrac{6}{12} = \dfrac{1}{2}$

Hence verified