question_answer 18)

                The students of Class VIII of a school donated Rs 2401 in all, for Prime Minister's National Relief Fund. Each student donated as many rupees as the number of students in the class. Find the number of students in the class.

Answer:

                Let the number of students in the class be \[x\]. Then rupees donated by each student = Rs \[x\]. \[\therefore \]  Rupees denoted by \[x\] students \[=\,\text{Rs}\,x\times x\] \[=\text{Rs}\,{{x}^{2}}\]   \[\therefore \] The students of class VIII of a school donated Rs 2401 for Prime Minister's National Relief Fund. \[\therefore \]  \[{{x}^{2}}=2401\] \[\Rightarrow \]               \[x=\sqrt{2401}\]. The prime factorisation of 2401 is

7	2401
7	343
7	49
	7

  \[2401=\underline{7\times 7}\times \underline{7\times 7}\] \[\therefore \]  \[x=\sqrt{2401}\,=\sqrt{\underline{7\times 7}\times \underline{7\times 7}}\] \[\Rightarrow \]               \[x=7\times 7=49\] Hence, the number of students in the class is 49.