A certain number of persons are seated in a row arranged vertically, all facing north. Ranjan is seated fourth from the left end of the row. There are two persons seated 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.

What is the position of Puja with respect to Ranjan?

Question

A certain number of persons are seated in a row arranged vertically, all facing north. Ranjan is seated fourth from the left end of the row. There are two persons seated 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.

What is the position of Puja with respect to Ranjan?

Accepted Answer

**Solution:**

1. Ranjan is seated 4th from the left end.

2. There are two persons between Ranjan and Seema, so Seema can be either 1st from the left (if Ranjan is 4th) or 7th from the left (if the row is long enough).

3. Puja sits immediately to the right of Seema.

4. The number of persons between Puja and Seema equals the number of persons between Dinesh and Puja.

5. Dinesh does not sit to the left of Ranjan, so Dinesh is either at Ranjan's position or to the right.

Let's assume the row has at least 8 persons for clarity.

- Since Ranjan is 4th, Seema must be 1st (4 - 3 = 1) or 7th (4 + 3 = 7) from the left. 
- If Seema is 1st, Puja is 2nd (immediate right of Seema).
- The number of persons between Puja and Seema is zero (since Puja is immediate right).
- Therefore, the number of persons between Dinesh and Puja is also zero, meaning Dinesh sits immediately next to Puja.
- Dinesh cannot be to the left of Ranjan (4th), so Dinesh must be to the right of Ranjan.

So, the seating from left to right is:
1. Seema
2. Puja
3. Dinesh
4. Ranjan

But this contradicts Dinesh not being to the left of Ranjan because Dinesh is at 3rd position, which is left of Ranjan (4th).

Hence, Seema must be 7th from the left.

- Seema is 7th, Puja is 8th (immediate right).
- Number of persons between Puja and Seema is zero.
- Number of persons between Dinesh and Puja is zero, so Dinesh sits immediately next to Puja.
- Dinesh cannot be to the left of Ranjan (4th), so Dinesh must be 9th or beyond.

Positions:
4th - Ranjan
7th - Seema
8th - Puja
9th - Dinesh

Now, find Puja's position relative to Ranjan:
- Puja is 8th, Ranjan is 4th.
- So, Puja is 4th to the right of Ranjan.

**Answer:** Puja is fourth to the right of Ranjan.

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