Question

If the numerator of a fraction is multiplied by 2 and the denominator is reduced by 5 the fraction

becomes 6/5. And , if the denominator is doubled and the numerator is increased by 8, the

fraction becomes 2/5. Find the fraction.

step by step instructions required otherwise reported​

Answer 1

Answer:

Step-by-step explanation:

Solution :-

Let the fraction be x/y.

According to the Question,

1st Equation,

⇒ 2x/(y - 5) = 6/5

⇒ 10x = 6y - 30

⇒ 5x = 3y - 15

⇒ 5x - 3y = - 15 .....(i)

2nd Equation,

⇒ (x + 8)/2y = 2/5

⇒ 5x + 40 = 4y

⇒ 5x - 4y = - 40 .....(ii)

Solving Eq (i) and (ii), we get

⇒ (5x - 3y) - (5x - 4y) = - 15 - (- 40)

⇒ 5x - 3y - 5x + 4y = - 15 + 40

⇒ b = 25 ... (iii)

Putting Eq (iii) in Eq (i), we get

⇒ 5x - (3 × 25) = - 15

⇒ 5x - 75 = - 15

⇒ 5x = - 15 + 75

⇒ 5x = 60

⇒ x = 12

Hence, the fraction is 12/25.

Answer 2

Answer:

Let the Numerator be N and Denominator be D of the Fraction respectively.

$\underline{\bigstar\:\:\textsf{According to the First Part :}}$

$:\implies\sf \dfrac{2N}{D-5}=\dfrac{6}{5}$

$:\implies\sf$ 5 × 2N = 6(D – 5)

$:\implies\sf$ 10N = 6D – 30 ⠀⠀⠀— eq. ( I )

$\rule{150}{1}$

$\underline{\bigstar\:\:\textsf{According to the Second Part :}}$

$:\implies\sf\dfrac{N + 8}{2D}=\dfrac{2}{5}$

$:\implies\sf$ 5(N + 8) = 2 × 2D

$:\implies\sf$ 5N + 40 = 4D

• Multiplying both term by 2

$:\implies\sf$ 2(5N + 40) = 2(4D)

$:\implies\sf$ 10N + 80 = 8D

• Putting value of 10N from eq. ( I )

$:\implies\sf$ 6D – 30 + 80 = 8D

$:\implies\sf$ 50 = 8D – 6D

$:\implies\sf$ 50 = 2D

• Dividing both term by 2

$:\implies\sf$ D = 25

$\rule{100}{0.8}$

$\underline{\bigstar\:\:\textsf{Using value of D in eq. ( I ) :}}$

⇢ 10N = 6D – 30

⇢ 10N = 6(25) – 30

⇢ 10N = 150 – 30

⇢ 10N = 120

• Dividing both term by 10

⇢ N = 12

$\rule{170}{2}$

$\bf{\dag}\:\underline{\boxed{\sf Original\: Fraction=\dfrac{N}{D}=\dfrac{\textsf{\textbf{12}}}{\textsf{\textbf{25}}}}}$