5. The numerator of a r
ational number is 8 less than its denominator. If the numerator is multiplied by 3 and 10 is added to the denominator, the new rational number is 25. Find the original rational number.
Answers
Correct Question :
The numerator of a rational number is 8 less than its denominator. If the numerator is multiplied by 3 and 10 is added to the denominator, the new rational number is 21/25. Find the original rational number.
Given :
- Numerator of a rational number is 8 less than its denominator.
- If the numerator is multiplied by 3 and 10 is added to the denominator the new rational number is 21/25.
To Find :
- Original Rational Number .
Solution :
As Given that Numerator of rational number is 8 less than its Denominator. So ,
Now ,
- If the numerator is multiplied by 3 and 10 is added to the denominator the new rational number is 21/25.
A.T.Q :
Value of x is 15 .
Therefore :
So , The Original Rational Number is 7/15 .
Given :-
The numerator of a r ational number is 8 less than its denominator. If the numerator is multiplied by 3 and 10 is added to the denominator, the new rational number is 21/25.
To Find :-
Rational number
Solution :-
Let the numerator be a
Then denominator = a + 8
Fraction = a/a + 8
When number is multiplied by 3 and 10 is added to denominator
3a/a + 8 + 10 = 21/25
3a/a + 18 = 21/25
25(3a) = 21(a + 18)
75a = 21a + 378
75a - 21a = 378
54a = 378
a = 378/54
a = 7
Then
Fraction = a/a + 8 = 7/15
Hence
Fraction is 7/15