Question

The numerator of a fraction is 2less than the denominator.lf 1is added to the denominator it becomes 1 by 2. Find the fraction

Answer 1

Let the numerator be x

The denominator will be (x + 2)

The Fraction will be x/(x+2)

According to the Question :-

x/(x+2+1) = 1/2

=> x/(x + 3) = 1/2

=> 2x = x + 3 [Cross Multiplying]

=> x = 3

Now we got the value of Numerator = 3

Denominator = x + 2 = 5

Hence the Fraction is 3/5 [ANS]

VERIFICATION

LHS = 3/5

= 3/(5 + 1) [Applying the condition]

= 3/6

= 1/2

= RHS [ So our answer is correct]

Answer 2

Let the denominator be x and numerator be ( x - 2 )

When one added to the denominator the fraction becomes 1/2.

$\longrightarrow\frac{x - 2}{x + 1} = \frac{1}{2}$

$\longrightarrow2(x - 2) = x + 1$

$\longrightarrow2x - 4 = x + 1$

$\longrightarrow2x - x = 4 + 1$

$\longrightarrow \: x = 5$

DENOMINATOR = 5

NUMERATOR = 3

$\huge\underline{ Fraction \: = \frac{3}{5} }$