Question

A Sum of rs 3000 is to be given in the form of 63 prizes. if the prize money is either rs 100 or rs 25 find the number of prizes of each type.

Answer 1

Let the number of prizes of money 100 be x, and the number of prizes of cost 25 be y ;
x+y = 63
y = 63-x -------(1)

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

63-x = 120-4x
4x-x = 120-63
3x = 57
x = 19

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

Hence the number of prizes of cost 100 each are 19 while other type of prizes are 44
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Answer 2

according to the question

total amount = 3000rs

total no. of prizes = 63

Let the no. of prizes for 100 rs = X

so , the no. of prizes for 25 rs. =y

X + Y =63 ................. eq 1

100x+25y =3000........eq2

y= 63-x ................. eq 3

substituting eq 3 in eq 2 , we get

100x +25( 63-x) = 3000

100x. + 1575 -25x = 3000

75x = 3000-1575

75x= 1425

X = 3000/1425

X=19...........eq 4

substituting eq 4 in eq 3

y=63-x

y=63-19

y=44

Therefore, the prizes are 19,44