Answer:
The denominator of a rational number is greater than its numerator by 10. The required rational number is [tex]\frac{11}{21}[/tex]
Solution:
Let the numerator be x.
And, denominator = x + 10
hence the original fraction is [tex]\frac{x}{x+10}[/tex]
Given that numerator is increased by 19 and denominator is decreased by 1 then the fraction is equal to [tex]\frac{3}{2}[/tex]
[tex]\frac{x+19}{x+10-1}=\frac{3}{2}[/tex]
[tex]\frac{x+19}{x+9}=\frac{3}{2}[/tex]
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 = [tex]\frac{x}{x+10}[/tex]
[tex]\begin{array}{l}{=\frac{11}{11+10}} \\\\ {=\frac{11}{21}}\end{array}[/tex]
Hence the required number is [tex]\frac{11}{21}[/tex]
