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A fraction becomes 1/3 when 1 is subtracted from the numerator and it becomes 1/4 when 8 is added to its denominator. The fraction obtained is:
- a)3 / 12
- b)4 / 12
- c)5 / 12
- d)7 / 12
Correct answer is option 'C'. Can you explain this answer?
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A fraction becomes 1/3 when 1 is subtracted from the numerator and it...
Let the fraction be x / y
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So, as per the question given,
(x - 1) / y = 1 / 3 => 3x – y = 3…………………(1)
x / (y + 8) = 1 / 4 => 4x – y = 8 ………………..(2)
Subtracting equation (1) from (2), we get
x = 5 ………………………………………….(3)
Using this value in equation (2), we get,
4 × 5 – y = 8
y = 12
Therefore, the fraction is 5 / 12.
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A fraction becomes 1/3 when 1 is subtracted from the numerator and it...
Given: A fraction becomes 1/3 when 1 is subtracted from the numerator and it becomes 1/4 when 8 is added to its denominator.
Let the original fraction be x/y.
When 1 is subtracted from the numerator, the new fraction becomes (x-1)/y. And this fraction is equal to 1/3. So, we can write:
(x-1)/y = 1/3
Solving for x, we get:
x = (y/3) + 1
When 8 is added to the denominator, the new fraction becomes x/(y+8). And this fraction is equal to 1/4. So, we can write:
x/(y+8) = 1/4
Substituting the value of x from the first equation, we get:
((y/3) + 1)/(y+8) = 1/4
Solving for y, we get:
y = 24/5
Substituting the value of y in the first equation, we get:
x = (24/5)/3 + 1
x = 5/12
Therefore, the fraction obtained is 5/12. Hence, the correct answer is option C.
Let the original fraction be x/y.
When 1 is subtracted from the numerator, the new fraction becomes (x-1)/y. And this fraction is equal to 1/3. So, we can write:
(x-1)/y = 1/3
Solving for x, we get:
x = (y/3) + 1
When 8 is added to the denominator, the new fraction becomes x/(y+8). And this fraction is equal to 1/4. So, we can write:
x/(y+8) = 1/4
Substituting the value of x from the first equation, we get:
((y/3) + 1)/(y+8) = 1/4
Solving for y, we get:
y = 24/5
Substituting the value of y in the first equation, we get:
x = (24/5)/3 + 1
x = 5/12
Therefore, the fraction obtained is 5/12. Hence, the correct answer is option C.
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A fraction becomes 1/3 when 1 is subtracted from the numerator and it becomes 1/4 when 8 is added to its denominator. The fraction obtained is:a)3 / 12b)4 / 12c)5 / 12d)7 / 12Correct answer is option 'C'. Can you explain this answer?
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