Students of a class collected as many paise from each student of class as is the number of students in that class. If the total collection is Rs. 59.29, then find the total number of students in the class.

55
65
77
80

hint Hint:

Total collection = Amount collected from each student * number of students

The correct answer is: 77

GIVEN-
Total collection = Rs. 59.29 = (59.29) * 100 = 5929
Amount collection from each student (in paise) = number of students in the class
TO FIND-
Number of students in the class.
SOLUTION-
Let the number of students = x ................................... (Equation i)
Amount collected from each student = Number of students in the class ............... (Given)
∴ Amount collected from each student = x .......... (From Equation i) ........................ (Equation ii)
Now, we know that-
Total collection = Amount collected from each student * number of students
∴ 5929 = x * x ................. (From Equations i & ii and given information)
∴ 5929 = x²
∴ 5929 = x²
∴ 77 * 77 = x²
∴ √(77 * 77) = x ..................................... (Taking square root both the sides)
∴ 77 = x
FINAL ANSWER-
Option 'b' i.e. '77' is the correct answer to the given question.

The least number that should be multiplied with 1008 to make it a perfect square is

Alternatively, the question can be solved by multiply numbers in each of the options given and then check whether the resultant number is a perfect square or not-
a. 5
1008 * 5 = 5040
We know that 5040 is not a perfect square because √5040 = 12√35.
b. 2
1008 * 2 = 2016
We know that 2016 is not a perfect square because √2016 = 12√14.
c. 7
1008 * 7 = 7056
We know that 7056 is a perfect square because √7056 = 84.
d. 8
1008 * 8 = 8064
We know that 8064 is not a perfect square because √8064 = 24√14.
FINAL ANSWER REMAINS THE SAME.