If the numerator of a fraction is increased by 200% and the denodminat

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
This question was previously asked in
UPSC CAPF – 2019
Let the original fraction be represented as n/d, where n is the numerator and d is the denominator.
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.
When a quantity is increased by X%, the new quantity is the original quantity plus X% of the original quantity, which is equivalent to Original Quantity * (1 + X/100). In this case, a 200% increase means the new value is (1 + 200/100) = 3 times the original. A 300% increase means the new value is (1 + 300/100) = 4 times the original.
Algebraic representation of word problems is key. Setting up the equation correctly based on the given percentages and the resulting fraction allows one to solve for the unknown original fraction. Simplifying the final fraction to its lowest terms is standard practice.