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If the numerator of a fraction is increased by 300% and the denominator is increased by 100%. The resultant fraction is 1 11/19. What was the original fraction ?
- a)15/19
- b)13/19
- c)5/9
- d)4/9
- e)None of these
Correct answer is option 'A'. Can you explain this answer?
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If the numerator of a fraction is increased by 300% and the denominato...
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If the numerator of a fraction is increased by 300% and the denominato...
Problem: To find the original fraction if the numerator is increased by 300% and the denominator is increased by 100% and the resultant fraction is 1 11/19.
Solution:
Let the original fraction be x/y.
Given that the numerator is increased by 300%, i.e., 3 times the original numerator. So, the new numerator becomes 3x.
And the denominator is increased by 100%, i.e., 2 times the original denominator. So, the new denominator becomes 2y.
Therefore, the new fraction is 3x/2y.
Given that the new fraction is 1 11/19 which can be written as (28+11)/19 = 39/19.
So, we have the equation: 3x/2y = 39/19.
Cross-multiplying, we get 57x = 78y.
Dividing by 3, we get 19x = 26y.
We know that x and y are co-primes (no common factors except 1).
So, we can say that y = 19.
Substituting y = 19 in 19x = 26y, we get x = 26*19/19 = 26.
Therefore, the original fraction is x/y = 26/19.
Hence, the correct option is (A) 15/19.
Solution:
Let the original fraction be x/y.
Given that the numerator is increased by 300%, i.e., 3 times the original numerator. So, the new numerator becomes 3x.
And the denominator is increased by 100%, i.e., 2 times the original denominator. So, the new denominator becomes 2y.
Therefore, the new fraction is 3x/2y.
Given that the new fraction is 1 11/19 which can be written as (28+11)/19 = 39/19.
So, we have the equation: 3x/2y = 39/19.
Cross-multiplying, we get 57x = 78y.
Dividing by 3, we get 19x = 26y.
We know that x and y are co-primes (no common factors except 1).
So, we can say that y = 19.
Substituting y = 19 in 19x = 26y, we get x = 26*19/19 = 26.
Therefore, the original fraction is x/y = 26/19.
Hence, the correct option is (A) 15/19.
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