Question

If the numerator is increased by1 its value is3/4.if denominator is increased by2 it's value is 1/2. Find the fraction

Answer 1

Answer:

${\boxed{\bold\red{Fraction = \dfrac{5}{8} }}}$

Step-by-step explanation:

Let the numerator be X and the denominator be Y.

${\underline{\underline{\bold{According\:to\:question:-}}}}$

$\tt Firstly:- \\\\\rightarrow\tt \dfrac{X + 1}{Y} =\dfrac{3}{4} \\\\\rightarrow\tt 3Y = 4(X + 1) \\\\\rightarrow\tt 3Y = 4X + 4 \\\\\rightarrow{\boxed{\bold\red{Y =\dfrac{4X + 4}{3}.........(i) }}}$

$\rule{300}{2}$

$\tt Secondly:- \\\\\rightarrow\tt \dfrac {X}{Y+2} =\dfrac{1}{2} \\\\\rightarrow\tt 2X = Y + 2 \\\\\tt *Putting\:values\:of\:(i)\:here:- \\\\\rightarrow\tt 2X = \dfrac{4X+4}{3} + 2 \\\\\rightarrow\tt 2X = \dfrac{4X+4+6}{3}\\\\\rightarrow\tt 2X = \dfrac{4X+10}{3} \\\\\rightarrow\tt 6X = 4X + 10 \\\\\rightarrow\tt 6X - 4X = 10 \\\\\rightarrow\tt 2X = 10 \\\\\rightarrow\tt X =\dfrac{10}{2} \\\\\rightarrow{\boxed{\bold\red{X = 5 }}}$

$\therefore\bold{\underline{Numerator(X) = 5}}$

$\tt *Putting\:value\:of\:X \:in\:(i) :-$

$\rightarrow\tt Y =\dfrac{4\times 5 + 4}{3} \\\\\rightarrow\tt Y =\dfrac{20+4}{3} \\\\\rightarrow\tt Y =\dfrac{24}{3} \\\\\rightarrow{\boxed{\bold\red{Y = 8 }}}$

$\therefore\bold{\underline{Denominator(Y) = 8}}$

$\therefore{\boxed{\bold\purple{Fraction\: \: =\dfrac{5}{8} }}}$

Answer 2

Question :-- If the numerator is increased by 1 its value is 3/4. if denominator is increased by 2 it's value is 1/2. Find the fraction ?

Answer :---

Let the original Fraction be N/D.

Case 1 :-

→ If the numerator is increased by 1 its value is 3/4 .

So,

→ (N+1)/D = 3/4

Cross - Multiply we get,

→ 4(N+1) = 3D

→ 4N + 4 = 3D

→ 3D - 4N = 4 ----------------------- Equation (1)

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Case 2 :-

→ if denominator is increased by 2 it's value is 1/2.

So,

→ N/(D+2) = 1/2

Cross - Multiply,

→ 2N = D + 2

→ 2N - D = 2 -------------------- Equation (2)

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Multiplying Equation (2) by 2 now, and than adding it into Equation (1) we get,

→ 2(2N -D) + (3D - 4N) = 2*2 + 4

→ 4N - 2D + 3D - 4N = 4 + 4

→ D = 8

Putting D value in Equation (2) now, we get,

→ 2N - 8 = 2

→ 2N = 2+8

→ 2N = 10

Dividing both sides by 2 ,

→ N = 5 .

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Hence, Original Fraction is = N/D = 5/8 .