Finding Original Fraction Based on Percentage Changes
Let the original fraction be represented algebraically as $\frac{x}{y}$.
Numerator Modification
The numerator $x$ is increased by 30%. The new numerator is calculated as:
$ x + (30\% \times x) = x + (0.30 \times x) = 1.30x $
Denominator Modification
The denominator $y$ is decreased by 35%. The new denominator is calculated as:
$ y - (35\% \times y) = y - (0.35 \times y) = 0.65y $
New Fraction Value
The resulting fraction after these modifications is $\frac{1.30x}{0.65y}$.
We are given that this new fraction equals $\frac{3}{15}$, which simplifies to $\frac{1}{5}$.
$ \frac{1.30x}{0.65y} = \frac{1}{5} $
Solving for the Original Fraction
First, simplify the numerical coefficients in the equation:
$ \frac{1.30}{0.65} = \frac{130}{65} = 2 $
Substitute this back into the equation:
$ 2 \times \frac{x}{y} = \frac{1}{5} $
To find the original fraction $\frac{x}{y}$, divide both sides by 2:
$ \frac{x}{y} = \frac{1}{5 \times 2} $
$ \frac{x}{y} = \frac{1}{10} $
Thus, the original fraction is $\frac{1}{10}$.
Similar Questions
- $1.236576576...$
can be written in the form of: - What is the sum of $\frac{1}{3}$, $\frac{4}{3}$ and $\frac{3}{4}$?
- Four persons A, B, C and D completed a task in $\frac{2}{3} \text{ h}, \frac{3}{4} \text{ h}, \frac{4}{5} \text{ h}$ and $\frac{1}{5} \text{ h}$ respectively. Who among the following took the highest amount of time to complete the task?
- The value of $\frac{4}{3} + \left( \frac{1}{1 + \frac{5}{6}} \right) - \frac{5}{4}$ is
What is the value of
$\frac{7}{9} - \frac{11}{12} + \frac{13}{16} - \frac{1}{8}$?
- How much does one need to add to $\frac{1}{2}$ to get $2$?
- The sum of the numerator and denominator of a fraction is 11. If the numerator is decreased by 1, the fraction becomes $\frac{1}{4}$. Find the fraction.
- Two-fifth of seven-seventeenth of three-fifth of a number is 84. Find 40% of that number.
- A beautician's income includes her salary and the tips she gets for her services. During a particular week, if her tips were $\frac{5}{4}$ of her salary, then what fraction of her income came from the tips?
- What smallest fraction should be added to $3\frac{2}{3} + 6\frac{7}{12} + 4\frac{9}{36} + 5 + 7\frac{1}{12}$ to make the sum a whole number?
Important Questions from Fractions
5 \(\frac{3}{4}\) + x + 2 \(\frac{1}{2}\) = 10 \(\frac{1}{8}\) Find the value of x.
Simplify the expression 441 ÷ \(\left[270 \div \frac{3}{7}+\left(17\div \frac{1}{3}\right)-\left(8\frac{1}{2}-\frac{5}{2}\right)\right]\)
Number 0.232323 can be written in rational form as:
Solve: \(\frac{1}{2}\) [{-2(2 + 3)*20}/2]
Match the following.
Column I
Column II
a.
Equivalent fraction of \(\frac{7}{12}\) is
i.
Proper fraction
b.
Equivalent fraction of \(\frac{9}{15}\) is
ii.
Improper fraction
c.
\(\frac{7}{11}\) is
iii.
\(\frac{21}{36}\)
d.
\(\frac{19}{5}\) is
iv.
\(\frac{3}{5}\)
