Question

The denominator of a fraction is greater than the numerator by 8. If the numerator is increased by 17 and denominator is decreased by 1, the number obtained is 3/2. Find the fraction.
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Answer 1

Answer:

13/21

Step-by-step explanation:

Given:-

• The denominator of a fraction is greater than the numerator by 8. If the numerator is increased by 17 and denominator is decreased by 1, the number obtained is 3/2.

To Find:-

• The fraction.

Solution:-

$\sf \bold{\: Let}$

$: \mapsto \bf\:N umerator \: be \: x \\ : \mapsto \bf \: Denominator = x + 8$

♠ As we know that -

$\bf \mapsto \: \pink{ \boxed{ \sf \bigstar Fraction = \frac{Numerator}{Denominator} }}$

Now, Adding 17 with Numerator and decreasing 1 from denominator.

$\rm \longrightarrow \maltese \: \purple{New \: numerator = x + 17 }\\ \\ \longrightarrow \rm \maltese \purple{ \:New \: denominator = {x + 8 - 1 } }\\ \leadsto \rm \purple{x + 7}$

$\leadsto \clubs \: \bf N ew \: fraction = \frac{3}{2}$

ACQ,

$\therefore \tt \frac{x +17 }{x + 7} = \frac{3}{2} \\ \\ \tt \dashrightarrow3(x + 7) = 2( x + 17) \\ \\ \tt \dashrightarrow3x + 21 = 2x + 34 \\ \\ \tt \dashrightarrow3x - 2x = 34 - 21 \\ \\ \tt \dashrightarrow \: \fcolorbox{purple}{green}{x = 13}$

$\leadsto \bigstar \bf \: Numerator = x = \color{aqua}13 \\ \\ \bf \leadsto \bigstar \: Denominator = x + 8 \\ \\ \twoheadrightarrow \: \bf13 + 8 \ \\ \\ \ \twoheadrightarrow \: \bf\pink{ 21} \\ \\ \\ \looparrowright \green{ \underbrace{ \bf\:Fraction = \frac{13}{21} }}$

Answer 2

Solution :

• The denominator of a fraction is greater than the numerator by 8.

• If the numerator is increased by 17 and the denominator is decreased by 1, the number obrained is 3/2.

We have to find the fraction.

Let us assume that the numerator of the fraction is x.

Then the denominator becomes x+8

The fraction is x/x+8

New fraction :

> x + 17/x+7 = 3/2

> 3(x+7) = 2( x + 17)

> 3x + 21 = 2x + 34

> x = 13

The fraction becomes 13/21

Answer : The required fraction is 13/21

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