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
Find the originalrational number.
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Answer :-
- The fraction is 7/15.
Given :-
- 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.
To Find :-
- Original fraction.
Solution :-
Let
- Denominator be x
- Numerator will be x - 8
Numerator is multiplied by 3
- 3 (x - 8)
10 is added to the denominator
- x + 10
→ New fraction is 21/25
According to question :-
⇒3 (x - 8)/x + 10 = 21/25
⇒3x - 24/x + 10 = 21/25
⇒25 (3x - 24) = 21 (x + 10)
⇒75x - 600 = 21x + 210
⇒75x - 21x = 210 + 600
⇒54x = 810
⇒x = 810/54
⇒x = 15
Now
- Denominator = x = 15
- Numerator = x - 8 = 15 - 8 = 7
Hence, the fraction is 7/15.
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