Jay and Vijay spent an equal amount of money to buy some pens and special pencils of the same quality from the same store, If Jay bought 3 pens and 5 pencils, and Vijay bought 2 pens and 7 pencils, then which one of the following is correct?

Correct Option

Let $P_{pen}$ represent the price of one pen and $P_{pencil}$ represent the price of one pencil.

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

• Jay's total expenditure: $3\times P_{pen}+5\times P_{pencil}$
• Vijay's total expenditure: $2\times P_{pen}+7\times P_{pencil}$

Equating their expenditures:

$3\times P_{pen}+5\times P_{pencil}=2\times P_{pen}+7\times P_{pencil}$

Rearranging the terms to determine the relationship between the prices:

$3\times P_{pen}-2\times P_{pen}=7\times P_{pencil}-5\times P_{pencil}$

$P_{pen}=2\times P_{pencil}$

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

Incorrect Options

• A pencil costs more than a pen:

  The derived relationship $P_{pen}=2\times P_{pencil}$ implies that $P_{pencil}=0.5\times P_{pen}$. 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 $P_{pen}=2\times P_{pencil}$, not three times. Hence, this statement is incorrect.