Question

The numerator and the denominator of a fraction are in the ratio3:2. If 3 is the added to the numerator and 2 is subtracted from the denominator, a new fraction is formed whose value is 9/4. Find the orginal fraction.​

Answer 1

Answer:

The fraction is 15/10.

Step-by-step explanation:

let x be the common ratio then the fraction becomes,

3x / 2x

ATP, (3x+3)/(2x-2) = 9/4

=> 4(3x+3) = 9(2x-2)

=> 12x + 12 = 18x - 18

=> 18x - 12x = 12 + 18

=> 6x = 30

=> x = 5

So, the fraction becomes

(3*5) / (2*5)

= 15 / 10

Answer 2

Solution:

Let numerator and denominator are in the ratio 3x:2x

According to the question,

$\tt{ \dfrac{3x + 3}{2x - 2} = \dfrac{9}{4} }$

On cross multiplication:

$\dashrightarrow \: \sf{4(3x + 3) = 9(2x - 2)}$

$\dashrightarrow \: \tt{12x + 12 = 18x - 18}$

$\dashrightarrow \: \sf{18 + 12 = 18x - 12x}$

$\dashrightarrow \: \tt{6x = 30}$

$\implies \boxed{ \bf{x = 5}}$

The original fraction:

Earlier we had considered the original fraction to be in the ratio of 3x:2x

So,

$\tt{\dfrac{3x}{2x} = \dfrac{3(5)}{2(5)} = \dfrac{15}{10} }$

$\therefore \boxed{ \bf{Original \: Fraction = \dfrac{15}{10} }}$

VERIFICATION:

Add 3 to the numerator and subtract 2 from denominator. This gives us:

$\tt{ \dfrac{15 + 3}{10 - 2} }$

$= \tt{ \dfrac{18}{8} }$

$= \tt{\dfrac{9}{4} }$

which was the fraction given in the question

★ HENCE VERIFIED ★

Know more:

A question similar to this:

https://brainly.in/question/39685283