Let $P_{p e n}$ represent the price of one pen and $P_{p e n c i l}$ represent the price of one pencil.

According to the problem statement, Jay and Vijay spent an equal amount of money.

Equating their expenditures:

$3 \times P_{p e n} + 5 \times P_{p e n c i l} = 2 \times P_{p e n} + 7 \times P_{p e n c i l}$

Rearranging the terms to determine the relationship between the prices:

$3 \times P_{p e n} - 2 \times P_{p e n} = 7 \times P_{p e n c i l} - 5 \times P_{p e n c i l}$

$P_{p e n} = 2 \times P_{p e n c i l}$

This equation indicates that the price of a pen is two times the price of a pencil.

A pencil costs more than a pen:

The derived relationship $P_{p e n} = 2 \times P_{p e n c i l}$ implies that $P_{p e n c i l} = 0.5 \times P_{p e n}$ . Therefore, a pencil costs half the price of a pen, making this statement incorrect.
The price of a pen is two times the price of a pencil:

This statement is identical to Option 2, which is the correct answer. In a standard multiple-choice question, only one option is designated as the primary correct answer.
The price of a pen is three times the Price of a pencil:

The calculation establishes that $P_{p e n} = 2 \times P_{p e n c i l}$ , not three times. Hence, this statement is incorrect.