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

How many persons are seated between Ranjan and Dinesh?

Question

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

How many persons are seated between Ranjan and Dinesh?

Accepted Answer

**Solution:**

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

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

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 must be seated at or to the right of Ranjan.

Let's analyze the positions:

- Since Ranjan is 4th, if Seema is 1st, Puja will be 2nd.
- Persons between Puja (2nd) and Seema (1st) = 0.
- Therefore, persons between Dinesh and Puja must also be 0, 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.

- Puja is 2nd, so Dinesh cannot be to the left of Ranjan if Dinesh is next to Puja on the left.

Hence, this arrangement is not possible.

Try Seema at 7th position:

- Ranjan is 4th, Seema is 7th, so 2 persons between them (5th and 6th).

- Puja sits immediately right of Seema, so Puja is 8th.

- Persons between Puja (8th) and Seema (7th) = 0.

- Therefore, persons between Dinesh and Puja = 0, so Dinesh sits immediately next to Puja.

- Dinesh cannot be left of Ranjan (4th), so Dinesh must be 9th.

Now, positions:

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

Number of persons between Ranjan (4th) and Dinesh (9th) = positions 5th, 6th, 7th, 8th = 4 persons.

**Answer:** 4

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