Understanding Student Positions in a Row

This problem involves determining the position of a student named Cintu in a row, based on the positions of other students, Amit and Bindu, and the number of students situated between them.

Analyzing Amit's and Bindu's Placements

We are given the following information:

• Amit is positioned 15^th from the left end of the row.
• Bindu is positioned 4^th from the right end of the row.
• There are exactly 3 students standing between Amit and Bindu.
• Cintu is situated immediately to the left of Amit.

Calculating the Total Number of Students

To find Cintu's position, we first need to determine the total number of students in the row. We can visualize the arrangement based on the given information:

The sequence can be represented as:

(Students to Amit's left) - Amit - (Students between Amit and Bindu) - Bindu - (Students to Bindu's right)

• Number of students to Amit's left = 15 - 1 = 14 students.
• Number of students to Bindu's right = 4 - 1 = 3 students.
• Number of students between Amit and Bindu = 3 students.

Therefore, the total number of students in the row ($N$) can be calculated as:

$$ N = (\text{Students left of Amit}) + \text{Amit} + (\text{Students between}) + \text{Bindu} + (\text{Students right of Bindu}) $$

Substituting the values:

$$ N = 14 + 1 + 3 + 1 + 3 = 22 \text{ students} $$

Determining Cintu's Position from the Left

We know that Cintu is just to the left of Amit.

Since Amit is 15^th from the left, Cintu, being immediately to his left, must be:

$$ \text{Cintu's position from left} = \text{Amit's position from left} - 1 $$

$$ \text{Cintu's position from left} = 15 - 1 = 14^{th} $$

Calculating Cintu's Position from the Right

Now we need to find Cintu's position from the right end of the row.

We know the total number of students is 22.

We also know Cintu's position from the left is 14^th.

The formula to find position from the right is:

$$ \text{Position from right} = (\text{Total number of students}) - (\text{Position from left}) + 1 $$

Let's apply this to Cintu:

$$ \text{Cintu's position from right} = 22 - 14 + 1 $$

$$ \text{Cintu's position from right} = 8 + 1 = 9^{th} $$

Alternatively, we can first find Amit's position from the right.

$$ \text{Amit's position from right} = (\text{Total number of students}) - (\text{Amit's position from left}) + 1 $$

$$ \text{Amit's position from right} = 22 - 15 + 1 = 8^{th} $$

Since Cintu is just to the left of Amit, Cintu is one position further away from the right end compared to Amit.

$$ \text{Cintu's position from right} = \text{Amit's position from right} + 1 $$

$$ \text{Cintu's position from right} = 8 + 1 = 9^{th} $$

Both methods confirm that Cintu is 9^th from the right.