Question

CLASSTUME Page No.
The
Sum of a numerator and denominator of a traction
js 18. the
denominaton is increase a by 2,
Fraction reduses to 13 - find the fraction.​

Answer 1

Correct Question:-

The sum of a numerator and denominator of a fraction is 18. If the denominator increased by 2, the fraction reduces to 1/3. Find the fraction.

Answer:-

Let the fraction be x/y.

Given:

Sum of the numerator and denominator = 18

⟹ x + y = 18

⟹ x = 18 - y -- equation (1)

And,

If the denominator is increased by 2 , the fraction reduces to 1/3.

⟹ x/y + 2 = 1/3

⟹ 3x = y + 2

Substitute the value of x from equation (1).

⟹ 3(18 - y) = y + 2

⟹ 54 - 3y = y + 2

⟹ 54 - 2 = y + 3y

⟹ 52 = 4y

⟹ 52/4 = y

⟹ 13 = y

Substitute the value of y in equation (1).

⟹ x = 18 - 13

⟹ x = 5

Therefore, the required fraction x/y is 5/13.

Answer 2

Correct Question :

• The sum of a numerator and denominator of a fraction is 18. The denominaton is increased by 2,fraction reduses to ⅓. Find the fraction.

Solution :

Let,

• Fraction = x/y.

Sum of numerator and denominator = 18

• x + y = 18

$\implies\sf{x = 18 - y..........(1)}$

And,

Denominator is increased by 2 to ⅓.

• x/y + 2 = 1/3.

$\implies\sf{3x = y + 2}$

Substitute,

• x = (18 - y)

$\implies\sf{3(18 - y) = y + 2}$

$\implies\sf{54 - 3y = y - 2}$

$\implies\sf{54 - 2 = y - 3y}$

$\implies\sf{54 = 4y}$

$\implies\sf{ \cfrac{54}{4} = y}$

$\implies\sf{y = 13}$

Substitute,

• y = 13.

$\implies\sf{x = 18 - 13}$

$\implies\sf{x = \: }{\textsf{\textbf{5.}}}$

Hence,

• The fraction = 5/13.