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 number of students in the class be $n$.
• Each student contributes $n$ rupees, so the initial total collection is $n \times n = n^2$ rupees.
• One student adds an extra Rs. 2, making the total collection $n^2 + 2$.
• The problem states the total collection is Rs. 443, so the equation is $n^2 + 2 = 443$.
• Solving for $n^2$, we get $n^2 = 443 - 2 = 441$.
• Taking the square root, $n = \sqrt{441} = 21$, which matches option (b).
Why the other options are wrong
- (a) 12
- If there were 12 students, the total would be $12^2 + 2 = 146$, not 443.
- (c) 43
- If there were 43 students, the total would be $43^2 + 2 = 1851$, not 443.
- (d) 45
- If there were 45 students, the total would be $45^2 + 2 = 2027$, not 443.
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.