If the numerator of a fraction is increased by 200% and the denodminator is increased by 300%, the resultant fraction is 9/17. What was the original fraction ?
10/17
11/17
12/17
13/17
Answer is Right!
Answer is Wrong!
This question was previously asked in
UPSC CAPF – 2019
The numerator is increased by 200%. This means the new numerator is the original numerator plus 200% of the original numerator.
New numerator = n + 200% of n = n + (200/100) * n = n + 2n = 3n.
The denominator is increased by 300%. This means the new denominator is the original denominator plus 300% of the original denominator.
New denominator = d + 300% of d = d + (300/100) * d = d + 3d = 4d.
The resultant fraction is the new numerator divided by the new denominator: (3n) / (4d).
We are given that the resultant fraction is 9/17.
So, (3n) / (4d) = 9/17.
We need to find the original fraction n/d. We can rearrange the equation to solve for n/d:
(3/4) * (n/d) = 9/17
Multiply both sides by the reciprocal of (3/4), which is (4/3):
n/d = (9/17) * (4/3)
n/d = (9 * 4) / (17 * 3)
n/d = 36 / 51
This fraction can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 3.
36 / 3 = 12
51 / 3 = 17
So, the original fraction was 12/17.