A certain number of persons are seated in a vertical row facing north. Ranjan is seated fourth from the left end. There are two persons between Ranjan and Seema. Puja sits immediately to the right of Seema. The number of persons between Puja and Seema is the same as the number of persons between Dinesh and Puja. Dinesh is not seated to the left of Ranjan.

How many persons are seated in the row?

Question

A certain number of persons are seated in a vertical row facing north. Ranjan is seated fourth from the left end. There are two persons between Ranjan and Seema. Puja sits immediately to the right of Seema. The number of persons between Puja and Seema is the same as the number of persons between Dinesh and Puja. Dinesh is not seated to the left of Ranjan.

How many persons are seated in the row?

Accepted Answer

**Solution:**

1. Ranjan is seated fourth from the left end. So, Ranjan's position is 4.

2. There are two persons between Ranjan and Seema. Since Ranjan is at position 4, Seema can be either at position 1 (4 - 3) or position 7 (4 + 3).

3. Puja sits immediately to the right of Seema. So, if Seema is at position 1, Puja is at position 2; if Seema is at position 7, Puja is at position 8.

4. The number of persons between Puja and Seema is the same as the number of persons between Dinesh and Puja.

- Since Puja is immediately right of Seema, the number of persons between them is zero.

- Therefore, the number of persons between Dinesh and Puja is also zero, meaning Dinesh sits immediately next to Puja.

5. Dinesh does not sit to the left of Ranjan, so Dinesh must be at a position greater than or equal to 4.

6. Let's test the two possibilities:

- If Seema is at position 1, Puja at 2, Dinesh must be immediately next to Puja, so at position 3.

But Dinesh at 3 is to the left of Ranjan (4), which is not allowed.

- If Seema is at position 7, Puja at 8, Dinesh must be immediately next to Puja, so at position 9.

Dinesh at 9 is to the right of Ranjan (4), which is allowed.

7. So the seating positions are:

1 - ?

2 - ?

3 - ?

4 - Ranjan

5 - ?

6 - ?

7 - Seema

8 - Puja

9 - Dinesh

8. The highest position occupied is 9, so there are 9 persons in the row.

**Answer:** 9

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