the numerator of a rational number is less than its denominator by 9. if the numerator becomes 3 times and the denominator is increased by 7 then the resultant number is 5/7.what was the original number
Answers
Step-by-step explanation:
Given :-
The numerator of a rational number is less than its denominator by 9. if the numerator becomes 3 times and the denominator is increased by 7 then the resultant number is 5/7.
To find :-
What was the original number ?
Solution :-
Let the denominator in a rational number be X
Then, the numerator in the rational number = 9 less than the denominator
Numerator= X-9
The rational number
= Numerator / Denominator
= (X-9)/X
Three times the numerator = 3(X-9)
The Denominator is Increased by 7 then Denominator will be X+7
Given that
The numerator becomes 3 times and the denominator is increased by 7 then the resultant number = 3(X-9)/(X+7)
According to the given problem
The resultant number = 5/7
=> 3(X-9)/(X+7) = 5/7
On applying cross multiplication then
=> 3(X-9)×7 = 5(X+7)
=> 21(X-9) = 5(X+7)
=> 21X-189 = 5X+35
=> 21X-5X = 35+189
=> 16X = 224
=> X = 224/16
=> X = 14
=> Denominator = 14
Numerator = X-9 = 14-9 = 5
Fraction = Numerator/Denominator = 5/14
Answer:-
The original rational number = 5/14
Check:-
The original rational number = 5/14
Denominator = 14
=> Denominator-9 = 14-9 = 5
=> Denominator-9 = Numerator
3×Numerator = 3×5 = 15
Denominator+7 = 14+7 = 21
The new fraction = 15/21 = (5×3)/(7×3)=5/7
Verified the given relations in the given problem
Used formulae:-
- Fraction = Numerator/Denominator