Question

the denominator of a rational number is greater than its numerator by 3.If numerator is increased by 14 and denominator is decreased by 3,the new number became 11/4. What is original numbers. SOLVE IN ONE VARIABLE

Answer 1

Hi...☺

Here is your answer...✌

Let the numerator of rational number be x

It is given that denominator is greater than its numerator by 3

Then,
denominator is x+3

$=> Fraction = \frac{x}{x + 3}$
Now
According to the question,

$\frac{x + 14} {x + 3 - 3} = \frac{11}{4} \\ \\ \frac{x + 14}{x} = \frac{11}{4} \\ \\ 4(x + 14) = 11x \\ \\ 4x + 56 = 11x \\ \\ 4x - 11x = - 56 \\ \\ - 7x = - 56 \\ \\ x = \frac{ - 56}{ - 7} \\ \\ x = 8$

Numerator = 8

Denominator = x+3 = 8+3 = 11

HENCE,

Required rational number is 8/11

Answer 2

Hii friend,

Let the numerator of the fraction be X.

Then the denominator of the fraction be (X+3)

Fraction = Numerator/Denominator = X/X+3

Numerator is increased by 14 then Numerator becomes (X+14).

And,

Denominator is decreased by 3 then the denominator becomes (X+3-3) = X.

Fraction = Numerator/Denominator = X+14/X

According to question,

X+14/X = 11/4

4(X+14) = 11X

4X + 56= 11X

11X-4X = 56

7X = 56

X = 56/7

X = 8

Numerator = X= 8

And,

Denominator = (X+3) = 8+3 = 11

Fraction = Numerator/Denominator = X/X+3 =8/11

HOPE IT WILL HELP YOU.... :-)