Question

A fraction becomes 1/3 When 1 is
Subtracted from the numerator and it becomes 1/4 when 8
is added to its denominatos. Find
fraction.​

Answer 1

✯The fraction = 5/12 ✯

Step-by-step explanation:

Given:

• A fraction becomes ⅓ when 1 is subtracted from the numerator and it becomes ¼ when 8 is added to its denominator.

To find:

• The fraction.

Solution:

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

Then,

• The fraction = x/y

✯${\underline{\sf{According\:to\:the\:1st\: condition:-}}}$

• A fraction becomes ⅓ when 1 is subtracted from the numerator.

$\implies\sf{\dfrac{x-1}{y}=\dfrac{1}{3}}$

$\implies\sf{y=3x-3.................eq(i)}$

✯${\underline{\sf{According\:to\:the\:2nd\: condition:-}}}$

• It becomes ¼ when 8 is added to its denominator.

$\implies\sf{\dfrac{x}{y+8}=\dfrac{1}{4}}$

$\implies\sf{4x=y+8}$

• [ Put y = 3x-3 from eq (i) ]

$\implies\sf{4x=3x-3+8}$

$\implies\sf{4x=3x+5}$

$\implies\sf{4x-3x=5}$

$\implies\sf{x=5}$

• Numerator of the fraction = 5

Now put x=5 in eq(i).

y = 3x - 3

$\implies\sf{y=3\times\:5-3}$

$\implies\sf{y=15-3}$

$\implies\sf{y=12}$

Therefore,

${\boxed{\sf{The\: fraction=\dfrac{5}{12}}}}$

__________________

Answer 2

Answer:

Let the Numerator be x and Denominator be y

So, Fraction will be x/y

❍ According to Question now,

→ Numerator - 1/y = 1/3

→ x - 1/y = 1/3

→ 3x - y = 3 [Equation (i)]

→ x/y + Denominator = 1/4

→ x/y + 8 = 1/4

→ 4x - y = 8 [Equation (ii)]

• Substracting equation (i) from equation (ii) we get :]

→ x = 5

• Substituting the value of x = 5 in equation (i) we get :]

→ 3x - y = 3

→ 3(5) - y = 3

→ 15 - y = 3

→ -y = 3 - 15

→ -y = -12

→ y = 12

Therefore,

• Required fraction = x/y = 5/12