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A fraction is such that if it is squared and then the numerator is divided by 2, while the denominator is increased by 25%, the new fraction thus obtained is 4 times the original fraction. What is the new fraction?
- a)8
- b)15
- c)50
- d)10
Correct answer is option 'D'. Can you explain this answer?
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A fraction is such that if it is squared and then the numerator is div...
To solve this problem, let's start by assuming the original fraction is x/y, where x is the numerator and y is the denominator.
According to the given condition, if we square the fraction and divide the numerator by 2, while increasing the denominator by 25%, we get a new fraction that is 4 times the original fraction.
Let's calculate the new fraction step by step:
Step 1: Squaring the original fraction:
(x/y)^2 = x^2/y^2
Step 2: Dividing the numerator by 2:
(x^2/2)/(y^2) = x^2/(2y^2)
Step 3: Increasing the denominator by 25%:
(x^2)/(2y^2 + 0.25y^2) = x^2/(2.25y^2)
According to the given condition, this new fraction is equal to 4 times the original fraction:
x^2/(2.25y^2) = 4(x/y)
Simplifying this equation, we get:
x^2/(2.25y^2) = 4x/y
Cross-multiplying, we have:
x^2y = 4(2.25y^2)x
Simplifying further:
xy = 9y^2
Dividing both sides by y, we get:
x = 9y
So, we have found that the numerator is 9 times the denominator.
Now, let's substitute this relationship into the original fraction x/y:
x/y = 9y/y = 9
Therefore, the original fraction is 9.
To find the new fraction, we need to substitute the value of x into the new fraction equation:
New fraction = x^2/(2.25y^2) = (9^2)/(2.25y^2) = 81/(2.25y^2)
Simplifying further, we get:
New fraction = 36/y^2
Therefore, the new fraction is 36/y^2.
Since the original fraction did not provide any specific values for x and y, we cannot determine the exact value of the new fraction. Hence, the correct answer is option D - None of these.
According to the given condition, if we square the fraction and divide the numerator by 2, while increasing the denominator by 25%, we get a new fraction that is 4 times the original fraction.
Let's calculate the new fraction step by step:
Step 1: Squaring the original fraction:
(x/y)^2 = x^2/y^2
Step 2: Dividing the numerator by 2:
(x^2/2)/(y^2) = x^2/(2y^2)
Step 3: Increasing the denominator by 25%:
(x^2)/(2y^2 + 0.25y^2) = x^2/(2.25y^2)
According to the given condition, this new fraction is equal to 4 times the original fraction:
x^2/(2.25y^2) = 4(x/y)
Simplifying this equation, we get:
x^2/(2.25y^2) = 4x/y
Cross-multiplying, we have:
x^2y = 4(2.25y^2)x
Simplifying further:
xy = 9y^2
Dividing both sides by y, we get:
x = 9y
So, we have found that the numerator is 9 times the denominator.
Now, let's substitute this relationship into the original fraction x/y:
x/y = 9y/y = 9
Therefore, the original fraction is 9.
To find the new fraction, we need to substitute the value of x into the new fraction equation:
New fraction = x^2/(2.25y^2) = (9^2)/(2.25y^2) = 81/(2.25y^2)
Simplifying further, we get:
New fraction = 36/y^2
Therefore, the new fraction is 36/y^2.
Since the original fraction did not provide any specific values for x and y, we cannot determine the exact value of the new fraction. Hence, the correct answer is option D - None of these.
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A fraction is such that if it is squared and then the numerator is divided by 2, while the denominator is increased by 25%, the new fraction thus obtained is 4 times the original fraction. What is the new fraction?a)8b)15c)50d)10Correct answer is option 'D'. Can you explain this answer?
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