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.
Answers
Topic
Linear Equations
Given
A sum of Rs. 3000 is to be given in the form of 63 prizes. The prize money is either Rs. 100 or Rs. 25.
To Find
The number of prizes of each type.
Solution
Total number of prizes = 63
Let number of prizes of Rs. 100 = x
Then,
The number of prizes of Rs. 25 = 63 - x
Now,
Total prize money = Rs. 3000
Sum in form of prize Rs. 100 = 100x
Sum in form of prize Rs. 25 = 25( 63 - x )
Note :- Sum for a prize can be calculated by ( Prize Money × Number of prize )
Total Prize Money = Sum in form of prize of Rs. 100 and Rs .25
3000 = 100x + 25( 63 - x )
3000 = 100x - 25x + 1575
3000 = 75x + 1575
3000 - 1575 = 75x
1425 = 75x
1425 / 75 = x
19 = x
So, total number of prizes of Rs. 100 is 19.
Now,
Calculating for number of prizes of Rs. 25.
Number of prizes of Rs. 25 = 63 -x
63 - x
63 - 19
44
So, total number of prizes of Rs. 25 is 44.
Answer
Total number of prizes of Rs. 25 is 44.
Total number of prizes of Rs. 100 is 19.
Given :
- A sum of Rs. 3000 is to be given in the form of 63 Prizes.
- Prize money is either Rs. 100 or Rs. 25
To find :
- The number of prizes of each type.
According to the question :
It is said that we will have two types here.
Let the prizes of Money Rs. 100 be ' x ' &
Let the prizes of Money Rs. 25 be ' y '
↦x = 100 & y = 25
↦x + y = Total No. of. prizes
⟹ x + y = 63
⟹ y = 63 - x ...... [ 1 st Eq ]
Then,
↦x + y = Total Amount
Substituting the values of ' x ' & ' y ' ,
↦100x + 25y = 3000
Divide all those numbers are multiple of 5
⟹ 4x + y = 120
⟹ y = 120 - 4x ...... [ 2 nd Eq ]
Substituting ' y ' value in [ 1 st Eq ] ,
⟹ y = 63 - x
⟹ 120 - 4x = 63 - x
⟹ 4x - x = 120 - 63
⟹ 3x = 57
⟹ x = 57 / 3
⟹ x = 19
Substituting ' x ' value in [ 1 nd Eq ] ,
⟹ y = 63 - x
⟹ y = 63 - 19
⟹ y = 44
The Prizes of Money Rs. 100 is 19 &
Prizes of Money Rs. 25 is 44.