Question

the numerator of a fraction is 7 less than the denominator.if 3 is added to the numerator and 2 is added to the denominator the value of the fraction becomes 2/3 .find the original fraction
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Answer 1

Answer:-

Let the fraction be x/y.

Given:

Numerator is 7 less than the denominator.

⟹ Numerator = Denominator - 7

⟹ x = y - 7 -- equation (1)

Also,

If 3 is added to numerator and 2 is added to denominator, the fraction becomes 2/3.

$\implies \sf \: \frac{x + 3}{y + 2} = \frac{2}{3}$

Substitute the value of x from equation (1).

$\: \implies \sf \: \frac{y - 7 + 3}{y + 2} = \frac{2}{3} \\ \\ \implies \sf \: 3(y - 4) = 2(y + 2) \\ \\ \implies \sf \: 3y - 12 = 2y + 4 \\ \\ \implies \sf \: 3y - 2y = 4 + 12 \\ \\ \implies \boxed{\sf \: y = 16}$

Substitute the value of y in equation (1).

⟹ x = y - 7

⟹ x = 16 - 7

⟹ x = 9

∴ The required fraction x/y is 9/16.

Answer 2

Answer:

$\Large{\boxed{\underline{\overline{\mathfrak{\star \: Question :- \: \star}}}}}$

The numerator of a fraction is 7 less than the denominator.if 3 is added to the numerator and 2 is added to the denominator the value of the fraction becomes 2/3 .find the original fraction.

$\huge\underline{\overline{\mid{\bold{\pink{ANSWER-}}\mid}}}$

$\Large{\underline{\underline{\bf{GiVen:-}}}}$

Numerator of a fraction is 2 less than the denominator.

If 1 is added to the numerator and 3 to the denominator then the becomes ⅔ .

$\Large{\underline{\underline{\bf{Find:-}}}}$

Find the Original fraction :-

$\Large{\underline{\underline{\bf{SoLuTion:-}}}}$

Let the denominator of fraction is 'x' then Numerator be

(x - 2) .

X - 2 / x

Now ,

As per the question :-

$\implies \sf \: \frac{x + 3}{y + 2} = \frac{2}{3}$

x - 1 / x + 3 = 2/3

3 ( x - 1 ) = 2 ( x + 3 )

3x - 3 = 2x + 6

3x - 2x = 3 + 6

x = 3 + 6

x = 9

$\huge\pink{\mathbb{hence}}}}$]

Original Fraction = 9 - 2 / 9

$\red{\bigstar}$ Original Fraction $\large\leadsto\boxed{\rm\purple{7/9 }}$