Question : When 8 is added to the numerator of a fraction and 12 is added to its denominator, the fraction becomes $\frac{1}{2}$. When 2 is subtracted from its numerator and denominator, the fraction becomes $\frac{1}{8}$. Find the original fraction.
Option 1: $\frac{9}{19}$
Option 2: $\frac{3}{10}$
Option 3: $\frac{4}{7}$
Option 4: $\frac{5}{11}$
New: SSC MTS 2024 Application Form OUT; Direct Link
Don't Miss: Month-wise Current Affairs | Upcoming Government Exams
New: Unlock 10% OFF on PTE Academic. Use Code: 'C360SPL10'
Correct Answer: $\frac{3}{10}$
Solution : Let the original fraction be $\frac{x}{y}$ where $x$ and $y$ are the numerator and denominator, respectively. According to the question, $\frac{x+8}{y+12}=\frac{1}{2}$ ⇒ $2x+16=y+12$ ⇒ $2x+4=y$ (equation 1) When 2 is subtracted from its numerator and denominator, the fraction becomes $\frac{1}{8}$. $\frac{x–2}{y–2}=\frac{1}{8}$ ⇒ $8x-16=y-2$ ⇒ $y=8x-14$ (equation 2) Substitute the value of $y$ in equation 2, ⇒ $2x+4=8x-14$ ⇒ $8x-2x=14+4$ ⇒ $6x=18$ ⇒ $x=3$ Substitute the value of $x$ in equation 1, ⇒ $2\times 3+4=y$ ⇒ $y=6+4=10$ The original fraction = $\frac{x}{y}=\frac{3}{10}$ Hence, the correct answer is $\frac{3}{10}$.
Application | Cutoff | Selection Process | Preparation Tips | Eligibility | Exam Pattern | Admit Card
Question : Determine the correct answer for $(\frac{1}{8}+\frac{9}{4}-3)$:
Question : The value of $\frac{2}{3} \times \frac{6}{5} \times \frac{10}{4}+\frac{1}{8}-\frac{3}{8}$ is:
Question : What is the value of $\frac{1}{7} \times \frac{1}{8} \div \frac{72}{51}$ of $(\frac{1}{9}+\frac{1}{8})+(\frac{63}{56} \times \frac{48}{72})$?
Question : Aadish can complete a work in 14 days. If he worked for 8 days, then what fraction of the work would be left?
Question : Which fraction among $\frac{2}{3}$,$\frac{4}{5}$ and $\frac{7}{11}$ is the largest?
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile