Question : A sum of INR 46, 800 is divided among A, B, C, and D in such a way that the ratio of the combined share of A and D to the combined share of B and C is 8: 5. The ratio of the share of B to that of C is 5 : 4. A receives INR 18,400. If $x$ is the difference between the shares of A and B and $y$ is the difference between the shares of C and D, then what is the value of ($x$ – $y$) (in INR)?

Option 1: 7000

Option 2: 6000

Option 3: 6500

Option 4: 5000

Question : A certain sum is divided between A, B, C, and D such that the ratio of the shares of A and B is 1 : 3, that of B and C is 2 : 5, and that of C and D is 2 : 3. If the difference between the shares of A and C is INR 3,510, then the share of D is:

Option 1: INR 4,320

Option 2: INR 3,240

Option 3: INR 6,075

Option 4: INR 4,050

Question : A sum of INR 1,250 has to be distributed among A, B, C, and D. The Total share of B and D is equal to $\frac{14}{11}$ of the total share of A and C. The share of D is half of the share of A. The share of C is 1.2 of the share of A. What are the shares of A, B, C and D respectively?

Option 1: INR 250, INR 575, INR 300, INR 125

Option 2: INR 350, INR 525, INR 300, INR 125

Option 3: INR 250, INR 525, INR 300, INR 125

Option 4: INR 250, INR 575, INR 300, INR 175

Question : Directions: If X × Y means that X is the father of Y, X ÷ Y means that X is the mother of Y, and X – Y means that X is the brother of Y then which of the following expressions shows that A is the father of C?

Option 1: A – B × C

Option 2: A ÷ C – B

Option 3: A × B ÷ C

Option 4: A × B – C

Question : If $27x^3-64y^3=(Ax+By)(C{x}^2-D{y}^2+12xy)$, then the value of $4A+B+3C+2D$ is:

Option 1: 5

Option 2: 3

Option 3: –3

Option 4: –4

Question : If $x+y=5$, $x^3+y^3=35$, what is the positive difference between $x$ and $y$?

Option 1: 0

Option 2: 1

Option 3: 5

Option 4: 6