Question

If 2 is added to the numerator and denominator it becomes 9/10 and if 3 is subtracted from the numerator and denominator it become 4/5. Find the fractions. ​

Answer 1

Step-by-step explanation:

here is ur ans. ans is 7/8

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Answer 2

Given :

• If 2 is added to the numerator and denominator it becomes 9/10.
• if 3 is subtracted from the numerator and denominator it become 4/5.

To Find :

• The original fraction.

Solution :

Let the numerator of the fraction be x.

Let the denominator of the fraction be y.

Fraction → $\mathtt{\dfrac{x}{y}}$

Case 1 :

Numerator →(x + 2)

Denominator →(y + 2)

Fraction →$\mathtt{\dfrac{x+2}{y+2}}$

Equation :

➣ $\mathtt{\dfrac{(x+2)}{(y+2)}\:=\:{\dfrac{9}{10}}}$

➣ $\mathtt{10(x+2)=9(y+2)}$

➣ $\mathtt{10x+20=9y+18}$

➣ $\mathtt{10x-9y=18-20}$

$\mathtt{10x-9y=-2}$ ___(1)

Case 2 :

Numerator → (x - 3)

Denominator →(y - 3)

Fraction → $\mathtt{\dfrac{x-3}{y-3}}$

Equation :

➣ $\mathtt{\dfrac{(x-3)}{(y-3)}\:=\:{\dfrac{4}{5}}}$

➣ $\mathtt{5(x-3)\:=4(y-3)}$

➣ $\mathtt{5x-15=4y-12}$

➣ $\mathtt{5x-4y=-12+15}$

$\mathtt{5x-4y=3}$ ____(2)

Multiply, equation 2 by 2,

$\mathtt{10x-20y=6}$ ___(3)

★ Solve equation 1 and equation 3 to find value of x and y.

★ Subtract equation 3 from equation 1,

$\mathtt{10x-9y-(10x-8y)\:=\:-2-6}$

➣ $\mathtt{10x-9y-10x+8y=-17}$

➣ $\mathtt{-y=-8}$

➣ $\mathtt{y=8}$

★ Substitute, y = 8 in equation 1,

➣ $\mathtt{10x-9y=-2}$

➣ $\mathtt{10x-9y=-2}$

➣ $\mathtt{10x-9(8)=-2}$

➣ $\mathtt{10x-72=-2}$

➣ $\mathtt{10x=-2+72}$

➣ $\mathtt{10x=70}$

➣ $\mathtt{x\:=\:{\cancel{\dfrac{70}{10}}}}$

➣ $\mathtt{x=7}$

Fraction :

$\large{\boxed{\sf{\red{Numerator\:=\:x\:=\:7}}}}$

$\large{\boxed{\sf{\red{Denominator\:=\:y\:=\:8}}}}$

$\large{\boxed{\sf{\red{ Fraction\:=\:{\dfrac{x}{y}\:=\:\dfrac{7}{8}}}}}}$