Question

if we add 1 to the numerator you and subtract one from the denominator a fraction becomes 1 it also become one by two only add one to the denominator what is the fraction
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Answer 1

3/5

Step-by-step explanation:

Given:

i) If we add 1 to the numerator and subtract one from the denominator a fraction becomes 1.

ii) If we add 1 to the denominator than fraction become 1/2.

To find:

The fraction

Solution:

Let, the fraction be x/y .

According to (i)

$\frac{x + 1}{y - 1} = 1 \\ \\ x + 1 = y - 1 \\ \\ x = y - 1 - 1 \\ \\ x = y - 2 \: \: \: .........(1)$

Now, According to (ii)

$\frac{x}{y + 1} = \frac{1}{2} \\ \\ 2x = y + 1 \\ \\ 2(y - 2) = y + 1 \: \: \: \: [\text{From.....1}] \\ \\ 2y - 4 = y + 1 \\ \\ 2y - y = 4 + 1 \\ \\ y = 5 \\ \\ \text{So,} \\ \\ x = y - 2 \\ \\ x = 5 - 2 = 3$

Hence, The required fraction is x/y = 3/5.

Answer 2

$\rule{200}3$

$\huge\tt{QUESTION:}$

• If we add 1 to the numerator you and subtract one from the denominator a fraction becomes 1 it also become one by two only add one to the denominator what is the fraction

$\rule{200}3$

$\huge\tt{SOLUTION:}$

Let us assume that the fraction is x/y.

According to (I) question,

$\begin{lgathered}↪\frac{x + 1}{y - 1} = 1 \\ ↪ x + 1 = y - 1 \\ ↪x = y - 1 - 1 \\↪ x = y - 2 \: \: \: (EQ.1)\end{lgathered}$

According to (II) question,

$\begin{lgathered}↪\frac{x}{y + 1} = \frac{1}{2} \\↪ 2x = y + 1 \\ ↪2(y - 2) = y + 1 \: \: \: \: [\text{From (EQ.1)}] \\↪ 2y - 4 = y + 1 \\ ↪2y - y = 4 + 1 \\ ↪ y = 5 \\ \\ \text{So,} \\ ↪ x = y - 2 \\ ↪ x = 5 - 2 = 3\end{lgathered}$

Hence,

The required fraction is x/y = 3/5.

$\rule{200}3$