The numerator and the denominator of a fraction are in the ratio of 3 : 2. If 3 is added to the numerator and 2 is subtracted from the denominator, a new fraction is formed whose value is 9/4.Find the original fraction.
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Answers
Answer:
The numerator and the denominator of a fraction are in the ratio 3:2 . If 3 is added to the numerator and 2 is subtracted from the denominator, a new fraction is formed whose value is 9/4. Find the original fraction. Hence, the required fraction is 15/10.
Step-by-step explanation:
Given :
The numerator and the denominator of a fraction are in the ratio 3 : 2.
If 3 is added to the numerator and 2 is subtracted from the denominator.
A new fraction is formed whose value is 9/4.
To find :
The original fraction.
Solution :
Let the numerator and denominator of the fraction be x and y.
Case 1 :-
>> The numerator and the denominator of a fraction are in the ratio of 3 : 2.
=> x : y = 3 : 2
=> x/y = 3/2
=> 2x - 3y = 0 - (1)
Case 2 :-
>> If 3 is added to the numerator and 2 is subtracted from the denominator, a new fraction is formed whose value is 9/4.
=> (x+3)/(y-2) = 9/4
=> 4(x+3) = 9(y-2)
=> 4x + 12 = 9y - 18
=> 4x - 9y = -4 - (2)
Subtracting (2) and (1) :-
>> 4x - 9y = -4
>> 2x - 3y = 0 ⇒ × 2
=> 4x - 9y = -4
=> 4x - 6y = 0
- 3y = 4
- y = 4/3
Substitute value of 4/3 in (1) :-
=> 2x - 3y = 0
=> 2x - 3(4/3) = 0
=> 2x - 4 = 0
- 2x = 4
- x = 2
Hence, the fraction is :-
=> x/y
- 2/(4/3)
- 6/4
- 3/2
∴ The original fraction is 3/2.