P invested ₹ 5000 per month for 6 months of a year and Q invested ₹ x per month for 8 months of the year in a partnership business. The profit is shared in proportion to the total investment made in that year.
If at the end of that investment year, Q receives \( \frac{4}{9} \) of the total profit, what is the value of \( x \) (in ₹)?
If at the end of that investment year, Q receives \( \frac{4}{9} \) of the total profit, what is the value of \( x \) (in ₹)?
Show Hint
- 2500
- 3000
- 4687
- 8437
The Correct Option is B
Solution and Explanation
Top Questions on Logical and Analytical Reasoning Skills
- Six friends—A, B, C, D, E, and F—are sitting around a circular table facing the center. The following information is known: A is sitting immediately to the left of B. C is sitting two places to the right of A. D is sitting opposite to E. F is not sitting next to C or D. Question: What is the position of F relative to A?
- CMAT - 2025
- Logical Reasoning
- Logical and Analytical Reasoning Skills
Eight students (P, Q, R, S, T, U, V, and W) are playing musical chairs. The figure indicates their order of position at the start of the game. They play the game by moving forward in a circle in the clockwise direction.
After the 1st round, the 4th student behind P leaves the game.
After the 2nd round, the 5th student behind Q leaves the game.
After the 3rd round, the 3rd student behind V leaves the game.
After the 4th round, the 4th student behind U leaves the game.
Who all are left in the game after the 4th round?
The 12 musical notes are given as \( C, C^\#, D, D^\#, E, F, F^\#, G, G^\#, A, A^\#, B \). Frequency of each note is \( \sqrt[12]{2} \) times the frequency of the previous note. If the frequency of the note C is 130.8 Hz, then the ratio of frequencies of notes F# and C is:
Shown on the left is a set of equations. Which option belongs to the same set?
- CEED - 2025
- Design Aptitude
- Logical and Analytical Reasoning Skills
Shown below is an arrangement of closely stacked spheres. Assume each one to be in contact with its immediate neighbour. What is the total number of points where the spheres touch each other?
- CEED - 2025
- Design Aptitude
- Logical and Analytical Reasoning Skills
Questions Asked in GATE EY exam
Two projectile protons \( P_1 \) and \( P_2 \), both with spin up (along the \( +z \)-direction), are scattered from another fixed target proton \( T \) with spin up at rest in the \( xy \)-plane, as shown in the figure. They scatter one at a time. The nuclear interaction potential between both the projectiles and the target proton is \( \hat{\lambda} \vec{L} \cdot \vec{S} \), where \( \vec{L} \) is the orbital angular momentum of the system with respect to the target, \( \vec{S} \) is the spin angular momentum of the system, and \( \lambda \) is a negative constant in appropriate units. Which one of the following is correct?
- GATE PH - 2025
- Quantum Mechanics
The figure shows an opamp circuit with a 5.1 V Zener diode in the feedback loop. The opamp runs from \( \pm 15 \, {V} \) supplies. If a \( +1 \, {V} \) signal is applied at the input, the output voltage (rounded off to one decimal place) is:
- GATE PH - 2025
- Electrical Circuits
A wheel of mass \( 4M \) and radius \( R \) is made of a thin uniform distribution of mass \( 3M \) at the rim and a point mass \( M \) at the center. The spokes of the wheel are massless. The center of mass of the wheel is connected to a horizontal massless rod of length \( 2R \), with one end fixed at \( O \), as shown in the figure. The wheel rolls without slipping on horizontal ground with angular speed \( \Omega \). If \( \vec{L} \) is the total angular momentum of the wheel about \( O \), then the magnitude \( \left| \frac{d\vec{L}}{dt} \right| = N(MR^2 \Omega^2) \). The value of \( N \) (in integer) is:
- GATE PH - 2025
- Rotational Motion
- The Hamiltonian for a one-dimensional system with mass \( m \), position \( q \), and momentum \( p \) is: \[ H(p, q) = \frac{p^2}{2m} + q^2 A(q) \] where \( A(q) \) is a real function of \( q \). If \[ m \frac{d^2 q}{dt^2} = -5q A(q), \] then \[ \frac{d A(q)}{d q} = n \frac{A(q)}{q}. \] The value of \( n \) (in integer) is:
- GATE PH - 2025
- Mechanics
- A system of three non-identical spin-\(\frac{1}{2}\) particles has the Hamiltonian
\[ H = \frac{A \hbar^2}{2} (\vec{S}_1 + \vec{S}_2) \cdot \vec{S}_3, \] where \( \vec{S}_1, \vec{S}_2, \vec{S}_3 \) are the spin operators of particles labelled 1, 2, and 3 respectively, and \( A \) is a constant with appropriate dimensions. The set of possible energy eigenvalues of the system is:- GATE PH - 2025
- Quantum Mechanics