Test: Ranking - 1 - CAT MCQ

The correct option is C 11th ; 10th
Rank of Ram from the last =23−13+1=11
and Rank of Shyam from the last =23−14+1=10

Given:

• There are 40 students in the class.
• Samir’s rank from the top is 12th.
• Alok is 8 ranks below Samir.

Step 1: Find Alok's rank from the top

Since Alok is 8 ranks below Samir, we add 8 to Samir's rank:

Alok’s rank from the top=12+8=20

Step 2: Find Alok's rank from the bottom

To find Alok's rank from the bottom, we subtract Alok's rank from the top from the total number of students and then add 1 (because if someone is ranked 1st from the top, they are 40th from the bottom):

Alok’s rank from the bottom=40−20+1=21

Final Answer:

Alok's rank from the bottom is 21st.

So, the correct answer is:

2. 21st

Step 1: Understand the initial positions

• A is 7th from the left.
• B is 9th from the right.

Step 2: After interchanging positions

• A becomes 11th from the left after interchanging with B.

Step 3: Determine B's new position

Since A and B interchange their positions, B's new position will be the original position of A, which was 7th from the left.

Step 4: Find the total number of people in the row

Now, since B is 9th from the right originally and after interchange, A becomes 11th from the left, we can use this information to find the total number of people in the row.

If A is now 11th from the left, and B is originally 9th from the right, the total number of people in the row can be calculated as:

Total number of people=Position of A from the left after interchange+Position of B from the right originally−1

Substitute the values:

Total number of people=11+9−1=19

Final Answer:

The total number of people in the row is 19.

So, the correct answer is:

2. 19

Given:

• Vijay is 14th from the front.
• Jack is 17th from the end.
• There are 48 persons in the queue.
• Mary is exactly in between Vijay and Jack.

Step 1: Calculate Jack's position from the front.

Since there are 48 people in the queue, Jack's position from the front can be calculated as:

Jack’s position from front=48−17+1=32\text{Jack's position from front} = 48 - 17 + 1 = 32Jack’s position from front=48−17+1=32

Step 2: Find the number of persons between Vijay and Jack.

Vijay is 14th from the front, and Jack is 32nd from the front. So, the number of persons between Vijay and Jack is:

32−14−1=17 persons between Vijay and Jack32 - 14 - 1 = 17 \text{ persons between Vijay and Jack}32−14−1=17 persons between Vijay and Jack

Step 3: Find Mary's position.

Since Mary is exactly in between Vijay and Jack, the number of persons between Vijay and Mary is half of the number of persons between Vijay and Jack.

Number of persons between Vijay and Mary=172=8.5\text{Number of persons between Vijay and Mary} = \frac{17}{2} = 8.5Number of persons between Vijay and Mary

Since we can't have half a person, we need to take the floor of the number for the exact count:

Number of persons between Vijay and Mary=8\text{Number of persons between Vijay and Mary} = 8Number of persons between Vijay and Mary=8

Final Answer:

The correct number of persons between Vijay and Mary is 8.

However, since one of the choices is 7 and another is 8, and the exact number was 8.5, the answer should be adjusted based on context. Since Mary is exactly between the two, 8 is the closest whole number and most likely correct. Thus, the correct answer is:

1. 8