Question

18.A fraction becomes 1/3 when one is subtracted from the numerator and it becomes 1/4 when eight is added to its denominator . Find the fraction​

Answer 1

Step-by-step explanation:

• let the denominator of fraction= y
• and the numerator of the fraction= x
• according to the question:

1. (x-1)/y = 1/3
2. x/(y+8) = 1/4

1. becomes 2. becomes

• 3(x-1) = y. 4(x)= 1(y+8)
• 3x-3=y. 4x=y+8
• 3x-y-3=0. 4x-y-8=0

subtract 1. from 2.

4x-y-8=0

-3x+y+3=0

=x+0-5= 0

• x-5=0

x=5. , put it in 1.

3(5)-y-3=0

15-3= y

12=y,.

y= 12

therefore the fraction is 5/12

Answer 2

GIVEN:

• A fraction becomes 1/3 when one is subtracted from the numerator.
• It becomes 1/4 when eight is added to its denominator.

TO FIND:

• What is the fraction ?

SOLUTION:

Let the numerator of the fraction be 'x' and the denominator be 'y'

• FRACTION = x/y

CASE:- 1)

❐ A fraction becomes 1/3 when one is subtracted from the numerator.

According to question:-

$\rm{\longrightarrow \dfrac{x-1}{y} = \dfrac{1}{3} }$

Use cross product

$\rm{\longrightarrow 3(x -1) = y }$

$\bf{\longrightarrow 3x -3 = y...1) }$

CASE:- 2)

❐ It becomes 1/4 when eight is added to its denominator.

According to question:-

$\rm{\longrightarrow \dfrac{x}{y+8} = \dfrac{1}{4} }$

Use cross product

$\rm{\longrightarrow 4x = y+8...2)}$

Put the value of 'y' from equation 1) in equation 2)

$\rm{\longrightarrow 4x = 3x -3+8}$

$\rm{\longrightarrow 4x -3x = 5 }$

$\bf{\longrightarrow x = 5 }$

Put the value of 'x' in equation 1)

$\rm{\longrightarrow 3 \times 5 -3 = y }$

$\rm{\longrightarrow 15 -3 = y }$

$\bf{\longrightarrow 12 = y }$

• FRACTION = 5/12

❝ Hence, the fraction formed is 5/12 ❞

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