CAT (DILR) ULTIMATE REVISION QUESTION BANK 2026

# Q1 of 66

DIRECTIONS for questions: Read the information given below and answer the question that follows.


A train travels from Station A to Station E, passing through stations B, C, and D, in that order. The train has a seating capacity of 200. A ticket may be booked from any station to any other station ahead on the route, but not to any earlier station.


A ticket from one station to another reserves one seat on every intermediate segment of the route. For example, a ticket from B to E reserves a seat in the intermediate segments B – C, C – D, and D – E.


The occupancy factor for a segment is the total number of seats reserved in the segment as a percentage of the seating capacity. The total number of seats reserved for any segment cannot exceed 200.


The following information is known.

1. Segment C – D had an occupancy factor of 95%. Only segment B – C had a higher occupancy factor.

2. Exactly 40 tickets were booked from B to C and 30 tickets were booked from B to E.

3. Among the seats reserved on segment D – E, exactly four-sevenths were from stations before C.

4. The number of tickets booked from A to C was equal to that booked from A to E, and it was higher than that from B to E.

5. No tickets were booked from A to B, from B to D and from D to E.

6. The number of tickets booked for any segment was a multiple of 10.


What was the occupancy factor for segment D – E?

Options
A.

35%

B.

70%

C.

84%

D.

77%

Show Answer
Correct Answer

70%

Solution

The correct answer is 70%.

Let's define the number of tickets booked from station X to station Y as TX,Y.

The total seating capacity of the train is 200. The occupancy of any segment is the sum of all tickets whose journey passes through that segment. Let's analyze the given conditions step-by-step.

Step 1: Determine the number of seats reserved on segments B-C and C-D.
From condition 1, the occupancy factor for segment C-D is 95%. This means the number of seats reserved is 0.95 × 200 = 190 seats. We are also told that only segment B-C had a higher occupancy factor. According to condition 6, all ticket numbers are multiples of 10, meaning the total seats reserved on any segment must also be a multiple of 10. The only multiple of 10 strictly greater than 190 and up to the maximum capacity of 200 is 200. Thus, segment B-C has an occupancy factor of 100%, and exactly 200 seats are reserved on it.

Step 2: Formulate the equation for segment B-C.
The tickets contributing to segment B-C are TA,C, TA,D, TA,E, TB,C, TB,D, and TB,E.
We are given the following values from the conditions:
- TB,C = 40 and TB,E = 30 (Condition 2)
- TB,D = 0 (Condition 5)

Using the total seats on B-C (200), we can write the equation:

TA,C+TA,D+TA,E+40+0+30=200

Simplifying this, we get:

TA,C+TA,D+TA,E=130

Step 3: Analyze the relationships between A's tickets.
Condition 4 states that TA,C = TA,E and TA,C > TB,E (which is 30). Let TA,C = TA,E = x. Therefore, x > 30. Since all ticket counts are multiples of 10, x can be 40, 50, 60, etc.

Substituting x into our simplified equation:

2x+TA,D=130

Step 4: Use the segment D-E occupancy condition.
The tickets contributing to segment D-E are TA,E, TB,E, TC,E, and TD,E. Condition 5 tells us TD,E = 0. So the total tickets on D-E is TA,E + TB,E + TC,E.

Condition 3 states that exactly four-sevenths of the seats reserved on D-E were from stations before C (which are stations A and B). So, the tickets from stations A and B that pass through D-E are TA,E and TB,E.

We can set up the proportion:

TA,E+TB,E=47×(TA,E+TB,E+TC,E)

We know TB,E = 30 and TA,E = x. Substituting these gives:

x+30=47×(x+30+TC,E)

Cross-multiplying by 7:

7(x+30)=4(x+30)+4TC,E

3(x+30)=4TC,E

Solving for TC,E:

TC,E=34×(x+30)

Step 5: Solve for x and calculate the segment D-E occupancy.
Since TC,E represents a number of tickets, it must be a whole number and a multiple of 10. This requires (x + 30) to be a multiple of 40 (so that when multiplied by 3/4, the result is a multiple of 10). Let's test the possible values of x (since x > 30 and a multiple of 10):
- If x = 40, then x + 30 = 70 (not divisible by 40).
- If x = 50, then x + 30 = 80 (divisible by 40!).
- If x = 60, then x + 30 = 90 (not divisible by 40).

Thus, x = 50. This means TA,E = 50.

Now we can calculate TC,E:

TC,E=34×80=60

The total number of seats reserved on segment D-E is:

TA,E+TB,E+TC,E=50+30+60=140

The occupancy factor for segment D-E is the total reserved seats as a percentage of the total capacity (200):

140200×100%=70%

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