Explanation:

To solve this problem, we need to find the price ratio of one pen to one pencil.

- Let's denote the price of a pen as "p" and the price of a pencil as "q".

- Initially, pens and pencils are bought in the ratio 5:3 for Rs 44.

- This means: 5p + 3q = 44.

- Later, they are bought in the ratio 3:5 for Rs 36.

- This means: 3p + 5q = 36.

- Now, solve these two equations simultaneously to find the ratio of p to q.

Solving the Equations:

Multiply the first equation (5p + 3q = 44) by 5:

\[ 25p + 15q = 220 \]

Multiply the second equation (3p + 5q = 36) by 3:

\[ 9p + 15q = 108 \]

Subtract the second equation from the first:

\[ 16p = 112 \]

\[ p = 7 \]

Substitute p = 7 back into one of the original equations to find q. Using 3p + 5q = 36:

\[ 3(7) + 5q = 36 \]

\[ 21 + 5q = 36 \]

\[ 5q = 15 \]

\[ q = 3 \]

Therefore, the ratio of the price of one pen (p) to one pencil (q) is 7:3.

Correct Answer: Option 2, 7:3