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 ?
- (a) A pencil costs more than a pen
- (b) The price of a pencil is equal to that of a pen
- (c) The price of a pen is two times the price of a pencil ✓ UPSC's answer
- (d) The price of a pen is three times the price of a pencil
Why the answer is (c)
• Let the price of a pen be P and the price of a pencil be C.
• Jay's total expenditure is 3P + 5C.
• Vijay's total expenditure is 2P + 7C.
• Since they spent equal amounts, equate the expressions: 3P + 5C = 2P + 7C.
• Subtract 2P from both sides to get P + 5C = 7C.
• Subtract 5C from both sides to get P = 2C, meaning the price of a pen is two times the price of a pencil.
Why the other options are wrong
- (a) A pencil costs more than a pen
- The calculation shows P = 2C, so a pen costs more than a pencil, not the other way around.
- (b) The price of a pencil is equal to that of a pen
- The equation P = 2C proves the prices are not equal.
- (d) The price of a pen is three times the price of a pencil
- The derived relationship is P = 2C, not P = 3C.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2021, held on 10 October 2021. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.