Question

the ratio of numerator and denominator of the rational number is 2:7 and if 4 is added to the numerator and 2 is subtracted from the denominator the rational number becomes 10/19. find the original number​

Answer 1

Given :

• Ratio of Numerator and Denominator of the Rational Number is 2:7 .
• If 4 is added to the numerator and 2 is subtracted from the denominator the rational number becomes 10/19.

To Find :

• Original Number .

Solution :

$\longmapsto\tt{Let\:the\:Numerator\:be=2x}$

$\longmapsto\tt{Let\:the\:Denominator\:be=7x}$

Now ,

• If 4 is added to the numerator and 2 is subtracted from the denominator the rational number becomes 10/19.

$\longmapsto\tt{Numerator=2x+4}$

$\longmapsto\tt{Denominator=7x-2}$

A.T.Q :

$\longmapsto\tt{\dfrac{2x+4}{7x-2}=\dfrac{10}{19}}$

$\longmapsto\tt{19(2x+4)=10(7x-2)}$

$\longmapsto\tt{38x+76=70x-20}$

$\longmapsto\tt{38x-70x=-20-76}$

$\longmapsto\tt{-32x=-96}$

$\longmapsto\tt{x=\cancel\dfrac{-96}{-32}}$

$\longmapsto\tt\bf{x=3}$

Value of x is 3 ..

Therefore :

$\longmapsto\tt{Numerator=2(3)}$

$\longmapsto\tt\bf{6}$

$\longmapsto\tt{Denominator=7(3)}$

$\longmapsto\tt\bf{21}$

So , The Original Number is 6/21 ..

Answer 2

Given:-

• Ratio of numerator and denominator of a rational number = 2:7

To find:-

The rational number

Assumption:-

Let the ratio constant be x

Numerator = 2x

Denominator = 7x

Solution:-

Ratio of numerator to denominator = 2x:7x

ATQ,

$\sf{\dfrac{2x+4}{7x-2} = \dfrac{10}{19}}$

By Cross-Multiplication,

= $\sf{19(2x+4) = 10(7x-2)}$

= $\sf{38x+76 = 70x - 20}$

= $\sf{38x-70x = -76-20}$

= $\sf{-32x = -96}$

= $\sf{x = \dfrac{-96}{-32}}$

= $\sf{x = 3}$

Now,

Numerator = 2x = 2×3 = 6

Denominator = 7x = 7×3 = 21

Therefore the fraction is $\sf{\bold{\dfrac{6}{21}}}$