Question

The numerator of a fraction is 3 less than the denominator. If 1 is added to both its numerator and denominator it becomes 1/2. Find the fraction.​

Answer 1

See the above attached attachment

Hope it helps

Answer 2

$\underline{\sf \fcolorbox{red}{pink}{ \huge{Solution :)}}}$

Let , the denominator of a fraction be x

So , numerator = x - 3

Thus , the rational number is (x - 3)/x

Condition : If 1 is added to both its numerator and denominator it becomes 1/2 , thus

$\sf \mapsto \frac{(x - 3 + 1)}{x + 1} = \frac{1}{2} \\ \\ \sf \mapsto</p><p>2(x - 2) = x + 1 \\ \\ \sf \mapsto</p><p>2x - 4 = x + 1 \\ \\ \sf \mapsto</p><p>x = 5</p><p>$

Hence , the fraction is 2/5

$\underline{\sf \fcolorbox{red}{pink}{ \huge{Verification :)}}}$

Adding 1 on both its numerator and denominator of fraction , we get

➡(2 + 1)/(5 + 1)

➡3/6

➡1/2

Hence verified

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