Question

a sum of ₹3000 is to be given in the form of 63 prizes if the prize money is either ₹100 or ₹25 find the number of prizes of each type

Answer 1

Let the number of prizes each of Rs.100 be x, and the number of prizes each of Rs.25 be y ;
then by question,
x + y = 63
y = 63 - x -------(1)

Cost of x prizes each of Rs.100= 100x
Cost of y prizes each of Rs.25 = 25y

Therefore, 100x + 25y = 3000
25(4x+y) = 3000
4x + y = 3000/25 = 120
y = 120 - 4x ------(2)

Replacing y = 63-x (as per eq1), we have
63 - x = 120 - 4x
4x - x = 120 - 63
3x = 57
x = 19

Hence y = 63-x = 63-19
y = 44

Thus the number of prizes each of Rs.100 = 19
& the number of prizes each of Rs.25 = 44