In a row of children, Deepti is ninth from the left and Kashish is thirteenth from the right. They exchange their positions and then Deepti becomes seventeenth from the left. Find the new position of Kashish from the right end of the row.

Options

A. 20th
B. 21th
C. 27th
D. None of these

Explanation

To solve the problem step by step, let's break it down:

### Step 1: Understand the initial positions
- Deepti is 9th from the left.
- Kashish is 13th from the right.

### Step 2: Determine the total number of children in the row
To find the total number of children in the row, we can use the formula:
\[ \text{Total number of children} = \text{Position from left} + \text{Position from right} - 1 \]
Substituting the known values:
\[ \text{Total number of children} = 9 + 13 - 1 = 21 \]

### Step 3: Analyze the exchange of positions
After Deepti and Kashish exchange their positions:
- Deepti becomes 17th from the left.
- Kashish takes Deepti's original position, which was 9th from the left.

### Step 4: Verify the new position of Deepti
Now, we need to confirm the total number of children again using Deepti’s new position:
- Deepti is now 17th from the left and was originally 13th from the right.
Using the same formula:
\[ \text{Total number of children} = 17 + 13 - 1 = 29 \]
This indicates that there was a mistake in our initial calculation. Let's correct it.

### Step 5: Recalculate the total number of children
Using Deepti's new position:
\[ \text{Total number of children} = 17 + 13 - 1 = 29 \]

### Step 6: Find Kashish's new position from the right
Now, we know that Kashish is now at Deepti's original position, which was 9th from the left. We can find Kashish's new position from the right using the total number of children:
\[ \text{Position from right} = \text{Total number of children} - \text{Position from left} + 1 \]
Substituting the values:
\[ \text{Position from right} = 29 - 9 + 1 = 21 \]

### Conclusion
Kashish's new position from the right end of the row is **21**.

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