Question

Which of the following statements is correct?

• A. The ATM placed at the (R-C, V2) intersection has a cash requirement of Rs. 9 Lakhs.
• B. There is no ATM placed at the (R-C, V2) intersection.
• C. The cash requirement of the ATM placed at the (R-C, V2) intersection cannot be uniquely determined.
• D. The ATM placed at the (R-C, V2) intersection has a cash requirement of Rs. 8 Lakhs.
• A. Only Statement A
• B. Both Statement A and Statement B
• C. Only Statement B
• D. Neither Statement A nor Statement B
• A. 5 km
• B. Either 4 km or 7 km
• C. 4 km
• D. 7 km

Answer 1

The Correct Option is A

The problem involves analyzing a network of roads and ATMs to determine the cash requirement at a specific intersection. Here's the solution:

Road	V1	V2	V3	Total Cash Requirement (Rs. Lakhs)
R-A	-	-	-	22
R-B	-	-	-	18
R-C	-	-	-	24
Total	15	10	19

The total cash requirement for the ATMs on roads R-A, R-B, and R-C are given as 22, 18, and 24 Lakhs respectively. Similarly, the total for vertical roads V1, V2, and V3 are 15, 10, and 19 Lakhs respectively. Using the additional information:

1. The ATMs with cash requirements Rs. 7 Lakhs and Rs. 15 Lakhs are on the same road.
2. The road distance between the ATM with the second highest cash requirement and the ATM at (R-C, V3) is 12 km.

From V2 and R-C having totals 10 and 24 respectively, with R-C - (R-C, V3) already known: 24 = x + 9 (R-C at V2) + ATM at (R-C, V3). Solving:

• Assume ATM with Rs. 15 Lakhs is on V1 or V3:
• If exact match is found for ATM(s) it checks intersection with R-B or R-C at V1 or V3:
• If Rs. 9 Lakhs found at (R-C, V2) or along R-C, maximizing satisfying conditions.

Thus verifying reveals:

The ATM placed at the (R-C, V2) intersection has a cash requirement of Rs. 9 Lakhs.

Answer 2

By reviewing the cash requirements of the ATMs and identifying those with Rs. 10 Lakhs or more, we find that three ATMs meet this criterion.

Answer 3

The given problem involves analyzing the placement of ATMs on a network of roads and identifying which of the given statements is definitely true. To solve the problem, let's use the provided details and verify each statement systematically.

First, consider the information given:

• R-A, R-B, and R-C are horizontal roads, and V1, V2, and V3 are vertical roads.
• Total cash requirement on R-A is 22 Lakhs.
• The ATMs with the minimum (7 Lakhs) and maximum (15 Lakhs) cash requirements are on the same road.
• The distance between the ATM with the second highest requirement and the ATM at the R-C and V3 intersection is 12 km.

Let's analyze each statement:

Statement A: Each of R-A, R-B, and R-C has two ATMs.

Statement B: Each of V1, V2, and V3 has two ATMs.

To verify, we need to place 6 ATMs on this 3x3 grid such that the conditions are satisfied.

Considering Statement A:

• R-A: Two possible known cash requirements are 7 and 15 Lakhs (if they are on R-A), as they must be on the same road.
• Total cash requirement for R-A is 22 Lakhs; hence, 7 and 15 fit perfectly, confirming two ATMs on R-A.
• For R-B and R-C, distribute remaining cash requirements such that each road gets two ATMs.

Checking Statement B:

• If each of V1, V2, and V3 should have two ATMs, it's more challenging to fit the requirements without violating the condition that ATMs number 7 and 15 must be on the same road, especially when aligning with R-B and R-C configurations.

Next, evaluate the intersection of R-C and V3 and the road distance of 12 km from the second highest ATM:

• This places constraints that further make the second configuration less feasible for statement B.

Thus, Statement A holds true logically without contradiction, while Statement B does not necessarily meet all the conditions definitively across all scenarios.

Correct option: Only Statement A

Answer 4

To determine the road distance between the ATMs with the second highest and second lowest cash requirements, we first need to find their positions based on the given conditions and constraints. Let's denote the cash requirements at intersections, represented as A1 to A6, where each ATM holds a distinct integer value in Rs. Lakhs.

The given conditions are:

• The minimum and maximum cash requirements (7 and 15 Lakhs respectively) are on the same road.
• The second highest ATM cash requirement is separated by a 12 km road distance from the ATM at the intersection of R-C and V3.

Further provided details:

• Total cash requirement for R-A = 22 Lakhs
• Total cash requirement for R-B = 15 Lakhs
• Total cash requirement for R-C = 25 Lakhs
• Total cash requirement for V1 = 27 Lakhs
• Total cash requirement for V2 = 24 Lakhs
• Total cash requirement for V3 = 11 Lakhs

Given such conditions and that each ATM's cash requirement differs:

• The second highest requirement should lie on-road such that the distance condition of 12 km as given is satisfied with the provided road structure.

Analyzed data shows the ATMs based on possible placement satisfying total road requirements and across specified intersections allow differences that could equate to either 4 km or 7 km as the potential solution.

Therefore, the best possible options given the constraints and structure equate in distance to either 4 or 7 km.

Answer 5

By analyzing the given data and the ATMs’ locations, three ATMs can be uniquely determined in both terms of their location and cash requirements.