Question

fraction become 8 by 11 if 3 is added to both numerator and denominator also if 3 is subtracted from the numerator and denominator it becomes 2 by 5 find fraction​

Answer 1

Answer

Let the original fraction be x / y

Then,

➡ (x+3) / (y+3) = 8/11 (given)

➡ 11(x+3) = 8(y+3)

➡ 11x + 33 = 8y + 24

➡ 11x - 8y = 24 - 33

➡ 11x - 8y = - 9 Eq.1

Also,

➡ (x-3) / (y-3) = 2/5 (given)

➡ 5(x-3) = 2(y-3)

➡ 5x - 15 = 2y - 6

➡ 5x - 2y = 15 - 6

➡ 5x - 2y = 9 Eq. 2

» Multiplying EQ. 2 by 4, we have:

➡ 20x - 8y = 36 Eq. 3

Subtracting EQ. 1 from EQ. 3, we get:

➡ 20x - 8y = 36

➡ 11x - 8y = - 9

⠀⠀- ⠀⠀+⠀⠀ +

_________________

➡ 9x = 45

➡ x = 45/9

➡ x = 5

Substituting the value of x in EQ.1, we get:

➡ 11x - 8y = -9

➡ (11×5) - 8y = -9

➡ 55 + 9 = 8y

➡ y = 64/8

➡ y = 8

✯ The original fraction $\</u><u>h</u><u>u</u><u>ge\</u><u>b</u><u>o</u><u>l</u><u>d</u><u>{\frac{</u><u>5</u><u>}{</u><u>8</u><u>}}$

Check:

Adding 3 to the numerator as well as denominator of original fraction 5/8

we get : (5 + 3) / (8 + 3) = 8/11 ✓

By subtracting 3 from the numerator as well as denominator of the original fraction 5/8

we get : (5 - 3) / (8 - 3) = 2/5 ✓

Answer 2

AnswEr :

⠀

The Original Fraction is $\large\bf{\frac{5}{8}}$

⠀

Explanation :

Let the Numerator be N and,

Denominator be D.

A.T.Q.

➟ $\large\bf{\dfrac{(N+3)}{(D+3)}}$ = $\large\bf{\dfrac{8}{11}}$

• By Cross Multiplication.

➟ 11(N + 3) = 8(D + 3)

➟ 11N + 33 = 8D + 24

➟ 11N - 8D = 24 - 33

➟ 11N - 8D = - 9 ⠀⠀(¡)

Again ;

➟ $\large\bf{\dfrac{(N-3)}{(D-3)}}$ = $\large\bf{\dfrac{2}{5}}$

• By Cross Multiplication.

➟ 5(N - 3) = 2(D - 3)

➟ 5N - 15 = 2D - 6

➟ 5N - 2D = - 6 + 15

➟ 5N - 2D = 9 ⠀⠀(¡¡)

━━━━━━━━━━━━━━━━━━━━━━━━

• Multiplying (¡¡) by 4.

➟ 4(5N - 2D) = 4 × 9

➟ 20N - 8D = 36 ⠀⠀(¡¡¡)

━━━━━━━━━━━━━━━━━━━━━━━━

• From Equation (¡) and (¡¡¡)

⟹ 20N - 8D = 36

⟹ 11N - 8D = - 9

⠀⠀-⠀⠀ +⠀⠀⠀+

_________________

⟹ 9N = 45

⟹ N = $\large{\cancel\dfrac{45}{9}}$

⟹ N = 5

━━━━━━━━━━━━━━━━━━━━━━━━

• Plugging the Value of N in Eq. (¡)

⟹ 11N - 8D = - 9

⟹ (11 × 5) - 8D = - 9

⟹ 55 - 8D = - 9

⟹ - 8D = - 9 + 55

⟹ 8D = 64

⟹ D = $\large{\cancel\dfrac{64}{8}}$

⟹ D = 8

━━━━━━━━━━━━━━━━━━━━━━━━

$\large\therefore$ The Original Fraction is 5 / 8.