If 3 is added to the numerator of a certain fraction, the value of the fraction becomes 3/5. If 9 is subtracted from the denominator of the original fraction, the value of this fraction becomes 2.5 times the value of the original fraction. What is the value of the original fraction?a)2/5b)3/2c)6/15d)5/6e)None of theseCorrect answer is option 'C'. Can you explain this answer?

Question

Answer

Let the original fraction be x/y

Instead of solving the equation, consider the fraction from the options and see which equation satisfies this condition.

Thus, the condition is satisfied only for option 3.
Hence, option 3.

Answer

Assume fraction is a/b,
given,
(a+3)/b=3/5 & a/(b-9) =2.5*a/b,

by solving this two equ.
we found a=6,b=15
so a/b=6/15

Answer

Given Information:

The fraction can be represented as x/y.

First Condition:

Adding 3 to the numerator: (x+3)/y = 3/5

Cross multiplying, we get:
5(x+3) = 3y
5x + 15 = 3y
y = (5x + 15)/3

Second Condition:

Subtracting 9 from the denominator: x/(y-9) = 2.5(x/y)

Substitute the value of y from the first condition:
x/((5x + 15)/3 - 9) = 2.5(x/(5x + 15)/3)

Simplify the equation:
3x/(5x + 15 - 27) = 2.5(3x/(5x + 15))
3x/(5x - 12) = 7.5x/(5x + 15)
3x(5x + 15) = 7.5x(5x - 12)
15x^2 + 45x = 37.5x^2 - 90x
22.5x^2 - 135x = 0
x(22.5x - 135) = 0
x = 0 or x = 6

Since the fraction cannot be 0, x = 6.

Substitute x = 6 back into the first condition:
y = (5*6 + 15)/3
y = 45/3
y = 15

Therefore, the original fraction is 6/15 which simplifies to 2/5. Hence, the correct answer is option C.

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