In a row of people all facing north, Rikshit is 31st from the right end and Palak is 32nd mfrom the right end. The number of people between Palak and Rikshit is same as the number of people between Palak and Huma. If Huma is 10th from the left end of the row, how many people are there in the row?

The correct option is 42.

Step-by-Step Explanation:

1. Position of Rikshit and Palak from the right end:

Rikshit is $31\text{st}$ from the right end.

Palak is $32\text{nd}$ from the right end.

2. Number of people between Palak and Rikshit:

Since Palak is 32nd from the right and Rikshit is 31st from the right, they are sitting adjacent to each other.

Therefore, the number of people between Palak and Rikshit = $32-31-1=0$.

3. Position of Huma:

The problem states that the number of people between Palak and Huma is the same as the number of people between Palak and Rikshit, which is $0$.

This means Huma and Palak are also sitting right next to each other.

Since Rikshit is 31st from the right and Palak is 32nd from the right, moving further away from the right end (towards the left) increases the position rank from the right end.

Thus, Huma must be $33\text{rd}$ from the right end.

4. Calculating the total number of people in the row:

We are given that Huma is $10\text{th}$ from the left end of the row.

Now, we have Huma's position from both ends:

Position from left end = $10$

Position from right end = $33$

Using the total people formula:

$\text{Total People}=\left(\text{Position from Left}\right)+\left(\text{Position from Right}\right)-1$

$\text{Total People}=10+33-1=42$

Hence, there are 42 people in the row.