Question

the neuminator and denominator are in ratio 3:4 and if denominator is increase by 3 and ratio become 3:5 find the rational no
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Answer 1

Step-by-step explanation:

let the value of numerator be = 3x

let the value of denominator be = 4x

if we increase in denominator by 3 so it is equal to 3:5 which is equal to 3x and 5x

so the equation will be:-

3x + 4x + 3 = 3x + 5x

7x + 3 = 8x

7x - 8x = -3

-x = -3

x = 3

putting the values of x in Numerator and denominator to find that's values so ,

Numerator = 3x = 3*3 = 9

Denominator = 4x =4*3 = 12 [Ans]

Additional

and you can verify that if you increase the no. 3 in its denominator it gets equal to ratio 3:5

how ?

3x is its numerator and 5x is its denominator

so 3x= 3*3 = 9

and 5x = 5*3 = 15

now compare our answer to this

numerator 9 9

------------- = -------

denominator 12 + 3 15

which is equals to

9/15 = 9/15

hence our answer is write

Answer 2

Let the rational number be x/y

Given:

• Numerator and denominator are in the ratio 3:4
• Denominator is increased by 3
• New ratio becomes 3:5

To find:

→ Rational number = ?

Method:

According to the question,

$\sf{\dfrac{x}{y} = \dfrac{3}{4} \: \: \: \dashrightarrow \: (equation \: 1)} \\ \\ \implies \sf{x = \dfrac{3y}{4} }$

Denominator is increased by 3.

$\sf{ \dfrac{x}{y + 3} = \dfrac{3}{5} } \\ \\ \implies \sf{ \dfrac{3y}{4(y + 3)} = \dfrac{3}{5} } \\ \\ \\ \implies \sf{ \dfrac{3y}{4y + 12} = \dfrac{3}{5} } \\ \\ \\ \implies \sf{5(3y) = 3(4y + 12)} \\ \\ \implies \sf{15y = 12y + 36} \\ \\ \implies \sf{15y - 12y = 36} \\ \\ \implies \sf{3y = 36} \\ \\ \therefore \sf{y = 12}$

Substitute the value of y in Equation 1 to find value of x.

$\sf{x = \dfrac{3y}{4} } \\ \\ \longrightarrow \: \sf{x = \frac{3(12)}{4} } \\ \\ \longrightarrow \: \sf{x = 9}$

$\therefore \boxed{ \bf{rational \: number = \dfrac{9}{12} }}$