Question

a fraction becomes 1/3 when 1 is subtracted from the numerator and it becomes 1/4 when 8 is added to its denominator. find the fraction

Answer 1

Answer:

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.

★ If 1 is subtracted from the numerator, the numerator will be (x-1).

According to the first condition,

$\implies \sf\: \dfrac{x - 1}{y} = \dfrac{1}{3} \\ \\ \implies \sf \: y = 3x - 3...........(1)$

★ If 8 is added to the denominator, the denominator will be (y+8).

$\implies \sf \: \dfrac{x}{y + 8} = \dfrac{1}{4} \\ \\ \implies \sf \: 4x = y + 8 \\ \\ \implies \sf \: 4x = 3x - 3 + 8 \: \{put \: y = 3x - 3 \: from \: eq(1) \} \\ \\ \implies \sf \: 4x - 3x = 5 \\ \\ \implies \sf \: x = 5$

Now put x = 5 in eq(1).

y = 3x-3

→ y = 3×5-3

→ y = 12

Therefore,

• The fraction = 5/12

Answer 2

Let Numerator be x & Denominator be y

So, Fraction is - $\frac{x}{y}$

Given that,

if 1 is subtracted from numerator fraction becomes ♤y=3x−3...........(1)

If 8 is added to the denominator, the denominator will be (y+8).

♤$\begin{gathered} \implies \sf \: \dfrac{x}{y + 8} = \dfrac{1}{4} \\ \\ \implies \sf \: 4x = y + 8 \\ \\ \implies \sf \: 4x = 3x - 3 + 8 \: \{put \: y = 3x - 3 \: from \: eq(1) \} \\ \\ \implies \sf \: 4x - 3x = 5 \\ \\ \implies \sf \: x = 5\end{gathered}$♧

♧4x=y+8

♧4x=3x−3+8

♧4x−3x=5

♧x=5

Now put x = 5

y = 3x-3

→ y = 3×5-3

→ y = 12

● Answer is 5/12