Question

the denominator of a rational number is greater than its numerator by 2. if the numerator is decreased by 3 and the denominator is increased by 4, the new rational number obtained is 2/5 . find the rational number.​

Answer 1

Step-by-step explanation:

Given :-

The denominator of a rational number is greater than its numerator by 2.

If the numerator is decreased by 3 and the denominator is increased by 4,then new rational number obtained is 2/5.

To find :-

The rational number.

Solution :-

Let the numerator of a rational number be X

Then , the denominator of the rational number

= Numerator + 2

Denominator = X+2

Then, The rational number = X/(X+2)

If the numerator is decreased by 3 then it will be (X-3)

If the denominator is increased by 4 then it will be (X+2+4) = (X+6)

Then the new rational number = (X-3)/(X+6)

According to the given problem

The new rational number = 2/5

=> (X-3)/(X+6) = 2/5

On applying cross multiplication then

=> 5(X-3) = 2(X+6)

=> 5X-15 = 2X+12

=> 5X-2X = 12+15

=> 3X = 27

=> X = 27/3

=> X = 9

The numerator = 9

The denominator = X+2 = 9+2 = 11

The required number = 9/11

Answer :-

The required rational number is 9/11

Check :-

The numerator = 9

The denominator = 11

The numerator is decreased by 3 then it will be 9-3 = 6

The denominator is increased by 4 then it will be

11+4 = 15

The new rational number = 6/15

= (2×3)/(5×3)

= 2/5

Verified the given relations in the given problem.

Answer 2

Information provided with us:

• The denominator of a rational number is greater than its numerator by 2.

• If the numerator is decreased by 3 and the denominator is increased by 4, the new rational number obtained is 2/5 .

What we have to find :

• ➡ The required rational number

Assumption :

Consider the original numerator be x .

Now :

According to first condition given in question .

• The denominator of a rational number is greater than its numerator by 2 .

Then original denominator ,

• ➡ ( x + 2 )

The original number ,

$\rm \implies \: \dfrac{x}{x + 2}$

According to second condition given in question .

• The numerator is decreased by 3

The new numerator

• ➡ ( x - 3)

According to third condition given in question .

• The denominator is increased by 4

The new denominator

• ➡ (x+2) + 4 = x + 6

The new number

$\rm \implies \: \dfrac{x - 3}{x + 6}$

According to the question ,

The new rational number obtained is 2/5

Here :

• By Using the given information, we get

$\rm \implies \: \dfrac{x - 3}{x + 6} = \dfrac{2}{5}$

• By cross multiplication ❌

$\rm \implies \: 5(x - 3) = 2(x + 6)$

$\rm \implies \: 5x - 15= 2x + 12$

$\rm \implies \: 5x - 2x= 12 + 15$

$\rm \implies \: 3 \: x=27$

$\rm \implies \: x = \dfrac{27}{3}$

$\bf \implies \: x =9$

Henceforth :

The original numerator

• ➡ x = 9

The original denominator

• ➡ x + 2 = 9 + 2 = 11

Therefore :

➡ The required original rational number

$\rm \implies \: \dfrac{x}{x+2} = \dfrac{9}{9+2}$

$\bf\implies \: \dfrac{9}{11}$

Now :

• By placing the value of x = 9 in $\rm \implies \: \dfrac{x - 3}{x + 6}$ we get ,

➡ The new rational number

$\rm \implies \: \dfrac{9- 3}{9+ 6} = \dfrac{6}{15}$

Therefore :

➡ The new rational number is

$\bf\implies \: \dfrac{6}{15}$