In aid of charity, every student in a class contributes as many rupees as the number of students in that class. With the additional contribution of Rs. 2 by one student only, the total collection is Rs. 443. Then how many students are there in the class ?
- (a) 12
- (b) 21 ✓ UPSC's answer
- (c) 43
- (d) 45
Why the answer is (b)
• Let the class have n students; each gives ₹n, so the collection is n × n = n².
• One student gives ₹2 extra: n² + 2 = 443, so n² = 441.
• n = 21, since 21 × 21 = 441.
• Hence 21 students, option (b).
Why the other options are wrong
- (a) 12
- With 12 students the total would be 12 × 12 + 2 = 146, not 443.
- (c) 43
- With 43 students the total would be 43 × 43 + 2 = 1,851.
- (d) 45
- With 45 students the total would be 45 × 45 + 2 = 2,027.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2016, held on 7 August 2016. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.