the dinomenater of a rational numbers is greater than its numerator by 8 . if the numerator increased by 17 and the dinomenater is decreased by 1 , the number is obtained is 3/2 find the rational numbers.
Answers
Step-by-step explanation:
Given :-
The dinomenater of a rational numbers is greater than its numerator by 8 . if the numerator increased by 17 and the dinomenater is decreased by 1 , the number is obtained is 3/2.
To find :-
Find the rational number ?
Solution :-
Let the numerator of a rational number be X
The denominator of the rational number
= Numerator + 8
= X+8
We have ,
Numerator = X
Denominator = X+8
The rational number = X/(X+8)
If the numerator is increased by 17 then the new numerator = X+17
If the denominator is decreased by 1 then the new denominator = X+8-1 = X+7
The new rational number = (X+17)/(X+7)
According to the given problem
The new rational number = 3/2
=> (X+17)/(X+7) = 3/2
On applying cross multiplication then
=> 3(X+7) = 2(X+17)
=> 3X+21 = 2X+34
=> 3X-2X = 34-21
=> X = 13
Numerator = 13
Denominator = X+8 = 13+8 = 21
The rational number = 13/21
Answer :-
The original rational number = 13/21
Check :-
The rational number = 13/21
Numerator = 13
Denominator = 21 = 13+8
Denominator = Numerator+8
If the numerator is increased by 17 then the new numerator = 13+17 = 30
If the denominator is decreased by 1 then the new denominator = 21-1= 20
The new rational number = 30/20 = 3/2
Verified the given relations in the given problem.
Answer:
13/21
Step-by-step explanation:
let the numerator be x
therefore the rational number becomes x/x+8
A.T.Q.,
x+17/x+8-1 =3/2
=> 2( x+17) = 3( x+7)
=> 2x+34 = 3x+21
after reversing ,
=> 3x +21 =2x +34
=> 3x-2x =34-21
=> x = 13 ( numerator)
=> x+8 = 21 ( denominator)
Therefore, the rational number is 13/21
THANKS.