In a total of 36 vehicles after one car there is one scooter . After 2nd car…

2023

In a total of 36 vehicles after one car there is one scooter . After 2nd car there will be two scooters and after 3rd car there will be 3 scooters so on . Then find the number of scooters in the right half of arrangement .

  1. A.

    12

  2. B.

    13

  3. C.

    14

  4. D.

    15

Attempted by 3 students.

Show answer & explanation

Correct answer: D

Answer: 15

Explanation: The pattern forms blocks where the nth car is followed by n scooters, so block n has 1 car + n scooters (n+1 vehicles).

  • Block 1: 1 car + 1 scooter → 2 vehicles (total 2)

  • Block 2: 1 car + 2 scooters → 3 vehicles (total 5)

  • Block 3: 1 car + 3 scooters → 4 vehicles (total 9)

  • Block 4: 1 car + 4 scooters → 5 vehicles (total 14)

  • Block 5: 1 car + 5 scooters → 6 vehicles (total 20)

  • Block 6: 1 car + 6 scooters → 7 vehicles (total 27)

  • Block 7: 1 car + 7 scooters → 8 vehicles (total 35)

After 7 blocks there are 35 vehicles, so the 36th vehicle is the next car (start of block 8).

We need the right half, i.e., the last 18 vehicles (positions 19–36). Listing those positions shows:

  • Positions 19–20: scooters

  • Position 21: car

  • Positions 22–27: scooters

  • Position 28: car

  • Positions 29–35: scooters

  • Position 36: car

Counting cars in the right half gives 3 cars (positions 21, 28, 36).

Therefore the number of scooters in the right half = 18 − 3 = 15.

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