Question

Sum of numerator and denominator of a feaction is 8. If 3 us added to both numerator and denominator the fraction becomes 3/4. Find fraction

Answer 1

$\bf{\red{\underline{\bf{Given:-}}}}$

• Sum of numerator and denominator of a feaction is 8. If 3 is added to both numerator and denominator the fraction becomes 3/4.

$\bf{\red{\underline{\bf{ToFind:-}}}}$

• Fraction

$\bf{\red{\underline{\bf{Solution:-}}}}$

Let the numerator be x and denominator be y

then,

➤ According to 1st condition :-

• Numerator + Denominator = 8

➭ x + y = 8

➭ x = 8 - y. --(1)

➤ According to 2nd condition :-

• Num + 3 / Den + 3 = 3/4

$\implies \: \frac{x + 3}{y + 3} = \frac{3}{4} \\ \\ \\ \implies \: 4(x + 3) = 3(y + 3) \\ \\ \\ \implies \: 4x + 12 = 3y + 9 \\ \\ \\ \implies \: 4x - 3y = 9 - 12 \\ \\ \\ \implies \: 4x - 3y = - 3$

➭ 4x - 3y = -3. --(2)

$\rule{200}2$

Put the value of (1) in (2) , we get,

➭ 4x - 3y = -3

➭ 4(8 - y) - 3y = -3

➭ 32 - 4y - 3y = -3

➭ 32 - 7y = -3

➭ -7y = -3 - 32

➭ -7y = -35

➭ y = -35/-7

➭ y = 5

Put y = 5 in (1) , we get,

➭ x = 8 - y

➭ x = 8 - 5

➭ x = 3

Hence,

• Numerator = x = 3
• Denominator = y = 5

Therefore,

• Fraction is x/y = 3/5

$\rule{200}3$

Answer 2

${ \huge{ \bold{ \underline{ \underline{ \orange{Question:-}}}}}}$

Sum of numerator and denominator of a feaction is 8. If 3 us added to both numerator and denominator the fraction becomes 3/4. Find fraction ..

${ \huge{ \bold{ \underline{ \underline{ \blue{Answer:-}}}}}}$

✒Given : -

• Sum of Numerator and Denominator is = 8..
• If 3 us added to both Numerator and denominator the fraction becomes 3/4..

✒To Find : -

• New Fraction = ?

✒Calculating : -

$\dashrightarrow\sf{Let\:Denominator\:be=x}$

$\dashrightarrow\sf{Let\:Numerator\:be=y}$

✒Now ,

$\leadsto\sf{{ \large{ \bold{ \underline{ \underline{ \purple{According\:to\:the\:Question:-}}}}}}}$

$\dashrightarrow\sf{x+y=8}$

$\dashrightarrow\sf{x=8-y}$ .... (1)

✒If 3 us added to both numerator and denominator the fraction becomes 3/4 ..

$\dashrightarrow\sf{Denominator=x+3}$

$\dashrightarrow\sf{Numerator=y+3}$

$\dashrightarrow\sf{\dfrac{y+3}{x+3}=\dfrac{3}{4}}$

$\dashrightarrow\sf{4(y+3)=3(x+3)}$

$\dashrightarrow\sf{4y+12=3x+9}$

$\dashrightarrow\sf{4y-3x=9-12}$

$\dashrightarrow\sf{4y-3x=-3}$ ..... (2)

✒On Substituting Value of Eq.1 in 2 ...

$\dashrightarrow\sf{4(8-y)-3y=-3}$

$\dashrightarrow\sf{32-4y-3y=-3}$

$\dashrightarrow\sf{32-7y=-3}$

$\dashrightarrow\sf{32+3=7y}$

$\dashrightarrow\sf{35=7y}$

$\dashrightarrow\sf{y=\cancel\dfrac{35}{6}}$

$\leadsto\sf{{ \large{ \bold{ \bold{ \bold{ \red{y=5}}}}}}}$

✒Now,Substituing Value of y = 5 in (1) ..

$\dashrightarrow\sf{x=8-5}$

$\dashrightarrow\sf{x=3}$

✒Therefore ,

$\dashrightarrow\sf{Denominator=y}$

$\dashrightarrow\sf{5}$

$\dashrightarrow\sf{Numerator=x}$

$\dashrightarrow\sf{3}$

✒The Fraction is 3/5 ..