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11 The numerator and the denominator of a fraction are in the ratio 3:2. I 3 is added to the numerator
and 2 is subtracted from the denominator, a new fraction is formed whose value is Find the original
fraction
Answers
CORRECT QUESTION.
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 denominator
a new fraction become 9/4 find the original
fraction.
EXPLANATION.
Let the numerator of a fraction be = x
Let the denominator of a fraction be = y
The numerator and denominator of a fraction
are in the ratio = 3:2
=> x/y = 3/2
=> 2x = 3y
=> 2x - 3y = 0 .....(1)
if 3 is added to the numerator and 2 is
subtract from denominator the new fraction
become = 9/4
=> x + 3 / y - 2 = 9/4
=> 4 ( x + 3 ) = 9 ( y - 2 )
=> 4x + 12 = 9y - 18
=> 4x - 9y = -30 .......(2)
From equation (1) and (2) we get,
multiply equation (1) by 2
multiply equation (2) by 1
we get,
=> 4x - 6y = 0
=> 4x - 9y = -30
we get,
=> 3y = 30
=> y = 10
put the value of y = 10 in equation (1)
we get,
=> 2x - 3(10) = 0
=> x = 15
Therefore,
original fraction = x/y = 15/10 = 3/2
Correct Question:
The numerator and the denominator of a fraction are in the ratio 3:2. I 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.
(Question is incomplete so we take a assumption that the formed fraction is 9/4 if we take 3/2 then it cancel out and we get answer as 0).
Step-by-step explanation:
The numerator and the denominator of a fraction are in the ratio 3:2.
Assume that the number is 3x and denominator be 2x.
Also said that, if 3 is added to the numerator and 2 is subtracted from the denominator, a new fraction is formed.
As per given condition,
→ (3x + 3)/(2x - 2) = 9/4
→ 4(3x + 3) = 9(2x - 2)
→ 12x + 12 = 18x - 18
→ 6x = 30
→ x = 5
Therefore,
- Numerator = 3x = 3(5) = 15
- Denominator = 2x = 2(5) = 10
Hence, the fraction is 15/10.