2021 CSAT, all questions

UPSC Prelims 2021 · CSAT

Question 53: Basic Numeracy

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 ?

aA pencil costs more than a pen
bThe price of a pencil is equal to that of a pen
cThe price of a pen is two times the price of a pencil
dThe price of a pen is three times the price of a pencil

AnswerUPSC’s answer is (c).

Let a pen cost p and a pencil cost c. Equal spending gives 3p + 5c = 2p + 7c. Subtract 2p and 5c from both sides: p = 2c. So a pen costs twice as much as a pencil. Check with c = 10 and p = 20: 3 × 20 + 5 × 10 = 110 and 2 × 20 + 7 × 10 = 110. Remember: when two baskets cost the same, equate them and cancel common terms to get the price ratio.

Why each option is right or wrong
  • (a) A pencil costs half a pen, so a pencil costs less than a pen.
  • (b) Equal prices would give 8 units to Jay and 9 to Vijay, which are unequal.
  • (c) Right: 3p + 5c = 2p + 7c gives p = 2c.
  • (d) p = 3c would give Jay 14c and Vijay 13c, which are unequal.

Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.

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Source: UPSC, Civil Services (Preliminary) Examination 2021, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.