Discussion
A fraction is such that if the numerator is multiplied by 2 and the denominator is reduced by 4 we get \(\frac{10}{3}\), but if the numerator is increased by 6 and the denominator is doubled we get \(\frac{11}{14}\), what is the fraction?
Answer: B
The fraction is \(\frac{5}{7}\).
Let the fraction be \(\frac{x}{y}\). The two conditions give
\[ \begin{aligned} \frac{2x}{y - 4} = \frac{10}{3} &\Rightarrow 6x = 10y - 40 \\ \frac{x + 6}{2y} = \frac{11}{14} &\Rightarrow 14x + 84 = 22y \end{aligned} \]
From the first, \(x = \frac{5y - 20}{3}\). Substituting in the second and multiplying through by 3 gives \(70y - 280 + 252 = 66y\), so \(4y = 28\), \(y = 7\) and \(x = 5\).
Check: \(\frac{10}{3}\) and \(\frac{11}{14}\) both come out. \(\frac{7}{5}\) is the reciprocal, and the other options fail the first condition.
Post your comment
Please log in or register to post a comment.
Examination Categories
- SSC Exams
- Banking Exams
- Teaching Exams
- Civil Services Exams
- Railways Exams
- Engineering Recruitment Exams
- Defence Exams
- State Government Exams
- Police Exams
- Insurance Exams
- Nursing Exams
- Other Government Exams
- NRA CET
- PG Entrance Exams
- Campus Placement
- MBA Entrance Exams
- CUET and UG Entrance
- Judiciary Exams
- Regulatory Body Exams
- Software Development