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…

Correct Option

Let $P_{pen}$Ppen​ represent the price of one pen and $P_{pencil}$Ppencil​ 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}$3×Ppen​+5×Ppencil​
• Vijay's total expenditure: $2 \times P_{pen} + 7 \times P_{pencil}$2×Ppen​+7×Ppencil​

Equating their expenditures:

$3 \times P_{pen} + 5 \times P_{pencil} = 2 \times P_{pen} + 7 \times P_{pencil}$3×Ppen​+5×Ppencil​=2×Ppen​+7×Ppencil​

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}$3×Ppen​−2×Ppen​=7×Ppencil​−5×Ppencil​

$P_{pen} = 2 \times P_{pencil}$Ppen​=2×Ppencil​

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 $P_{pen} = 2 \times P_{pencil}$Ppen​=2×Ppencil​ implies that $P_{pencil} = 0.5 \times P_{pen}$Ppencil​=0.5×Ppen​. 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 $P_{pen} = 2 \times P_{pencil}$Ppen​=2×Ppencil​, not three times. Hence, this statement is incorrect.