A bookseller sold 'a' number of Geography textbooks at the rate of ₹ x per book, 'a + 2' number of History textbooks at the rate of ₹ (x + 2) per book and 'a - 2' number of Mathematics textbooks at the rate of ₹ (x - 2) per book. What is his total sale in ₹?
- (a) 3x + 3a
- (b) 3ax + 8 ✓ UPSC's answer
- (c) 9ax
- (d) x³ a³
Why the answer is (b)
• Calculate the revenue from Geography textbooks: a books sold at ₹x each gives a total of ax.
• Calculate the revenue from History textbooks: (a + 2) books sold at ₹(x + 2) each gives (a + 2)(x + 2) = ax + 2a + 2x + 4.
• Calculate the revenue from Mathematics textbooks: (a - 2) books sold at ₹(x - 2) each gives (a - 2)(x - 2) = ax - 2a - 2x + 4.
• Sum the three revenues: ax + (ax + 2a + 2x + 4) + (ax - 2a - 2x + 4).
• Combine like terms: the 2a and -2a cancel out, the 2x and -2x cancel out, leaving 3ax + 4 + 4.
• The final total sale is 3ax + 8, which corresponds to option (b).
Why the other options are wrong
- (a) 3x + 3a
- Option (a) incorrectly assumes the total quantity is 3 and the price is x, ignoring the specific quantities and prices for each subject.
- (c) 9ax
- Option (c) ignores the constant terms (+4 and +4) resulting from the expansion of the History and Mathematics sales.
- (d) x³ a³
- Option (d) incorrectly multiplies the variables as cubes rather than summing the linear products of quantity and price.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2018, held on 3 June 2018. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.