IAS 2016 — CSAT Maths

Correct Option (2)

Let the number of students in the class be $x$x. According to the problem statement, each student contributes an amount in rupees equal to the number of students. Therefore, the total contribution from all students, excluding any additional amount, is $x \times x = x^2$x×x=x2 rupees.

An additional contribution of 2 rupees was made by one student. The total collection is stated to be 443 rupees.

Thus, the total collection can be represented by the equation:

$$x^2 + 2 = 443$$x2+2=443

To determine the sum contributed solely by the students based on their number, subtract the additional contribution from the total collection:

$$x^2 = 443 - 2$$x2=443−2

$$x^2 = 441$$x2=441

To find the number of students, take the square root of 441:

$$x = \sqrt{441}$$x=441​

$$x = \pm 21$$x=±21

Since the number of students cannot be a negative value, the positive root is considered.

Therefore, the number of students in the class is 21.

Incorrect Options:

The fundamental equation derived from the problem statement is $x^2 = 441$x2=441, where $x$x represents the number of students. Let's evaluate the other options:

• If the number of students were 12 (Option 1), the total contribution based on the number of students would be $12^2 = 144$122=144. Adding the additional 2 rupees, the total collection would be $144 + 2 = 146$144+2=146, which does not match the given total of 443 rupees.
• If the number of students were 43 (Option 3), the total contribution based on the number of students would be $43^2 = 1849$432=1849. Adding the additional 2 rupees, the total collection would be $1849 + 2 = 1851$1849+2=1851, which does not match the given total of 443 rupees.
• If the number of students were 45 (Option 4), the total contribution based on the number of students would be $45^2 = 2025$452=2025. Adding the additional 2 rupees, the total collection would be $2025 + 2 = 2027$2025+2=2027, which does not match the given total of 443 rupees.

Only $x = 21$x=21 satisfies the condition $x^2 = 441$x2=441, resulting in a total collection of $21^2 + 2 = 441 + 2 = 443$212+2=441+2=443 rupees, consistent with the problem statement.