Question

TO
3
21. A fractionis such that if the numerator is multiplied
by 3 and the denominator is reduced by 3, we get
18
, but if the numerator is increased by 8 and the
2
denominator is doubled, we get 5
Find the fraction
ultipy 2
E​

Answer 1

Correct Question:

• A fraction is such that if the numerator is multiplied by 3 and the denominator is reduced by 3, we get 18/11, but if the numerator is increased by 8 and the denominator is doubled, we get 2/5. Find the fraction.

Answer:

The required fraction will be 12/25

Step-by-step explanation:

Let us assume that the numerator of the fraction be x.

And the denominator of the fraction be y.

Given that:

• A fractions such that if the numerator is multiplied by 3 and the denominator is reduced by 3, we get 18/11.

→ 3x/(y - 3) = 18/11

→ 3x × 11 = 18(y - 3)

→ 33x = 18y - 54

→ 3 × 11x = 3(6y - 18)

→ x = (6y - 18)/11

Given that:

• But if the numerator is increased by 8 and the denominator is doubled, we get 2/5.

→ (x + 8)/2y = 2/5

→ 5(x + 8) = 2(2y)

→ 5(x + 8) = 4y

→ 5x + 40 = 4y

→ 5x = 4y - 40

→ x = (4y - 40)/5

Comparing both the equation:

(6y - 18)/11 = (4y - 40)/5

→ 5(6y - 18) = 11(4y - 40)

→ 30y - 90 = 44y - 440

→ 44y - 30y = - 90 + 440

→ 14y = 350

→ y = 350/14

→ y = 25

Here we get: Denominator = 25

Substituting the value of y in any equation:

→ x = (6 × 25 - 18)/11 or x = (4 × 25 - 40)/5

→ x = (150 - 18)/11 or x = (100 - 40)/5

→ x = 132/11 or x = 60/5

→ x = 12 or x = 12

Here we get: Numerator = 12

We know that:

• Fraction = Numerator / Denominator
• Fraction = 12/25

Answer 2

Correct Question:-

• A fraction is such that if the numerator is multiplied by 3 and the denominator is reduced by 3, we get 18/11, but if the numerator is increased by 8 and the denominator is doubled, we get 2/5. Find the fraction.

Given:-

• A fraction such that if the numerator is multiplied by 3 and the denominator is reduced by 3, we get 18/11,
• But if the numerator is increased by 8 and the denominator is doubled, we get 2/5.

To Find:-

• The Fraction = ?

Solution:-

Let the fraction be x/y

According to the given conditions

we have,

$\sf \: \frac{3x}{y - 3} = \frac{18}{11}$

And

$\sf \: \frac{x + 8}{2y} = \frac{2}{5}$

$\to\sf \: 11x - 6y - 18 \: and \: 5x + 40 = 4y$

$\to \: \sf \: 11x - 6y + 18 = 0 \: and \: 5x - 4y + 40 = 0$

Using Cross multiplication,

We have

$\to \: \sf \: \frac{x}{( - 6) \times 40 - ( - 4) \times 18} = \frac{ - y}{11 \times 40 - 5 \times 18}$

$\to \: \sf \: \frac{1}{11 \times ( - 4) - 5 \times ( - 6)}$

$\implies \: \sf \: \frac{x}{ - 240 + 72} = \frac{ - y}{440 - 90} = \frac{1}{ - 44 + 30}$

$\implies\sf \: \frac{x}{ - 168} = \frac{y}{ - 350} = \frac{1}{ - 14}$

$\implies\sf \: x = \frac{ - 168}{ - 14} \: and \: y \: = \frac{ - 350}{ - 14}$

$\implies\star{\boxed{\sf{x = 12 \: and \: y = 25}}}$

Hence,

• The required fraction is 12/25

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