A certain number of persons are seated in a vertical row, all 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 does not sit 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, all 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 does not sit to the left of Ranjan.

How many persons are seated in the row?

Accepted Answer

**Solution:**

1. Ranjan is seated 4th from the left end. So, his position is fixed at 4.

2. There are two persons between Ranjan and Seema. This means 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 2; if Seema is at 7, Puja is at 8.

4. The number of persons between Puja and Seema equals the number of persons between Dinesh and Puja. Since Puja is immediately right of Seema, there are zero persons between Puja and Seema.

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

6. Dinesh does not sit to the left of Ranjan (position 4), so Dinesh must be to the right of Ranjan.

7. Considering Seema at position 7, Puja at 8, Dinesh must be at 9 (immediately right of Puja).

8. The seating positions occupied are: 1 (?), 2 (?), 3 (?), 4 (Ranjan), 7 (Seema), 8 (Puja), 9 (Dinesh).

9. To accommodate all these positions, the total number of persons must be at least 9.

**Answer:** 9

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