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There is a fraction such that if we add 11/30 to it then it gets reverted. Further if we subtract 1 from numerator then the fraction becomes 2/3. What is the fraction?
- a)13/18
- b)7/9
- c)5/6
- d)8/11
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
There is a fraction such that if we add 11/30 to it then it gets reve...
Let the fraction = m/n
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According to the 1st condition; m/n + 11/30= n/m ...(1)
According to the 2nd condition; (m - 1)/n = ⅔
=> 3m - 3 = 2n
=> 3m - 2n = 3 ...(2)
By solving equation 1,
=> 30m2 + 11mn - 30n2 = 0
=> (6m - 5n)(5m + 6n) = 0
we get the value of m/n = 5/6, -6/5
applying condition(2), m/n = (5 - 1)/6 = 4/6 = 2/3
Hence the required fraction = m/n = 5/6
Most Upvoted Answer
There is a fraction such that if we add 11/30 to it then it gets reve...
Given Information:
- There is a fraction that, when 11/30 is added to it, gets reverted.
- If 1 is subtracted from the numerator of the fraction, it becomes 2/3.
To Find:
The fraction that satisfies the given conditions.
Assumption:
Let the fraction be represented as a/b, where a is the numerator and b is the denominator.
Analysis:
According to the given conditions:
1) When 11/30 is added to the fraction, it gets reverted.
This can be expressed mathematically as a/b + 11/30 = b/a.
Multiplying both sides by (30ab) to eliminate the denominators, we get:
30a^2 + 11ab = 30b^2
2) If 1 is subtracted from the numerator, the fraction becomes 2/3.
Mathematically, this can be represented as (a-1)/b = 2/3.
Cross-multiplying, we have:
3(a-1) = 2b
3a - 3 = 2b
Solution:
We have two equations:
1) 30a^2 + 11ab = 30b^2
2) 3a - 3 = 2b
Solving these equations simultaneously will give us the values of a and b.
Method 1: Substitution Method
From equation 2, we can express a in terms of b:
3a = 2b + 3
a = (2b + 3)/3
Substituting this value of a in equation 1, we get:
30((2b + 3)/3)^2 + 11b((2b + 3)/3) = 30b^2
Simplifying and rearranging the equation, we obtain:
4b^2 + 18b + 9 = 10b^2
10b^2 - 4b^2 + 18b - 10b^2 + 9 = 0
6b^2 + 18b + 9 = 0
Dividing both sides by 3:
2b^2 + 6b + 3 = 0
Solving this quadratic equation, we find:
b = -1/2 or -3/2
Substituting these values of b back into equation 2, we can find the corresponding values of a.
Method 2: Elimination Method
From equation 2, we can express a in terms of b:
a = (2b + 3)/3
Substituting this value of a in equation 1, we get:
30((2b + 3)/3)^2 + 11b((2b + 3)/3) = 30b^2
Simplifying and rearranging the equation, we obtain:
4b^2 + 18b + 9 = 10b^2
Rearranging the equation, we have:
6b^2 + 18b + 9 = 0
Dividing both sides by 3:
2b^2 + 6b + 3 = 0
Solving
- There is a fraction that, when 11/30 is added to it, gets reverted.
- If 1 is subtracted from the numerator of the fraction, it becomes 2/3.
To Find:
The fraction that satisfies the given conditions.
Assumption:
Let the fraction be represented as a/b, where a is the numerator and b is the denominator.
Analysis:
According to the given conditions:
1) When 11/30 is added to the fraction, it gets reverted.
This can be expressed mathematically as a/b + 11/30 = b/a.
Multiplying both sides by (30ab) to eliminate the denominators, we get:
30a^2 + 11ab = 30b^2
2) If 1 is subtracted from the numerator, the fraction becomes 2/3.
Mathematically, this can be represented as (a-1)/b = 2/3.
Cross-multiplying, we have:
3(a-1) = 2b
3a - 3 = 2b
Solution:
We have two equations:
1) 30a^2 + 11ab = 30b^2
2) 3a - 3 = 2b
Solving these equations simultaneously will give us the values of a and b.
Method 1: Substitution Method
From equation 2, we can express a in terms of b:
3a = 2b + 3
a = (2b + 3)/3
Substituting this value of a in equation 1, we get:
30((2b + 3)/3)^2 + 11b((2b + 3)/3) = 30b^2
Simplifying and rearranging the equation, we obtain:
4b^2 + 18b + 9 = 10b^2
10b^2 - 4b^2 + 18b - 10b^2 + 9 = 0
6b^2 + 18b + 9 = 0
Dividing both sides by 3:
2b^2 + 6b + 3 = 0
Solving this quadratic equation, we find:
b = -1/2 or -3/2
Substituting these values of b back into equation 2, we can find the corresponding values of a.
Method 2: Elimination Method
From equation 2, we can express a in terms of b:
a = (2b + 3)/3
Substituting this value of a in equation 1, we get:
30((2b + 3)/3)^2 + 11b((2b + 3)/3) = 30b^2
Simplifying and rearranging the equation, we obtain:
4b^2 + 18b + 9 = 10b^2
Rearranging the equation, we have:
6b^2 + 18b + 9 = 0
Dividing both sides by 3:
2b^2 + 6b + 3 = 0
Solving
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There is a fraction such that if we add 11/30 to it then it gets reverted. Further if we subtract 1 from numerator then the fraction becomes 2/3. What is the fraction?a)13/18b)7/9c)5/6d)8/11Correct answer is option 'C'. Can you explain this answer?
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