The denominator of a rational number is greater than its numerator by 3 if numerator and denominator both are increased by 5 then the new number become3/4 find the 6
Answers
Answer:
Solution:
Let the numerator of a rational number be x then the denominator is x+8.
Therefore, Rational number = \frac{x}{x+8}
x+8
x
According to the question,
\frac{x+17}{x+8-1}=\frac{3}{2}
x+8−1
x+17
=
2
3
\Rightarrow\ \frac{x+17}{x+7}=\frac{3}{2}⇒
x+7
x+17
=
2
3
\Rightarrow\ 2\left(x+17\right)=3\left(x+7\right)⇒ 2(x+17)=3(x+7)
\Rightarrow\ 2x+34=3x+21⇒ 2x+34=3x+21
\Rightarrow\ 2x-3x=21-34⇒ 2x−3x=21−34
\Rightarrow\ -x=-13⇒ −x=−13
\Rightarrow\ x=13⇒ x=13
Hence, the required rational number
=\ \frac{x}{x+8}=\frac{13}{13+8}=\frac{13}{21}=
x+8
x
=
13+8
13
=
21
13
Let the required number be x/y
.
Since denominator of the number is greater than its numerator by 3.
∴y=x+3.....(1)
Also,k
(x−3)/(y+2)= 1/5
5(x−3)=y+2
5x−15=(x+3)+2
5x−15=x+5
5x−x=15+5
⇒x=20/4 =5
Substituting the value of x in equation (1), we have
y=5+3=8
Therefore,
Required no. = 5/8