Question

The denominator of a rational number is greater than its numerator by 10. If the

Answer 1

Answer:

The denominator of a rational number is greater than its numerator by 10. The required rational number is $\frac{11}{21}$

Solution:

Let the numerator be x.

And, denominator = x + 10

hence the original fraction is $\frac{x}{x+10}$

Given that numerator is increased by 19 and denominator is decreased by 1 then the fraction is equal to $\frac{3}{2}$

$\frac{x+19}{x+10-1}=\frac{3}{2}$

$\frac{x+19}{x+9}=\frac{3}{2}$

Evaluate the above expression

2(x+19)=3(x+9)  

Multiply 2 with (x+19) and Multiply 3 with (x+9)

2x+38=3x+27

Keep x in one side and constant in other side. so that we can find the value of x.

2x-3x=27-38

-x= -11

Eliminating the ‘-‘sign

Therefore x=11.

Hence, required fraction =  $\frac{x}{x+10}$

$\begin{array}{l}{=\frac{11}{11+10}} \\\\ {=\frac{11}{21}}\end{array}$

Hence the required number is $\frac{11}{21}$

Answer 2

Answer:

3 / 4

Step-by-step explanation:

The original no. = x / x + 10   [ Numerator is taken as x ]

The new no. = x + 19 / (x + 10) - 1

                     = x + 19 / x + 9 = 3 / 2

Equation-

x + 19 / x + 9 = 3 / 2

By cross multiplying, we get,

2x + 38 = 3x + 27

2x - 3x = 27 - 38

       -x = -11

        x = 11

Therefore the original no. = ( 11 + 19 ) / ( 11 + 19 + 10 )

                                           = 30 / 40

                                           = 3 / 4

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