Question

There are 200 Prizes of Rs. 100 and Rs. 50 only. If the total amount spent on the prizes is Rs. 12,000, the number of prizes of Rs. 100 is:

• A. 50
• B. 100
• C. 40
• D. 60

Hint:

When solving mixture problems, create an equation based on the total cost and the individual costs of the items, then solve for the unknown quantity.

Answer 1

The Correct Option is C

Let the number of prizes of Rs. 100 be \( x \), and the number of prizes of Rs. 50 be \( 200 - x \). 
Step 1: The total amount spent on the prizes is: \[ 100x + 50(200 - x) = 12000 \] 
Step 2: Simplify the equation: \[ 100x + 10000 - 50x = 12000 \] \[ 50x + 10000 = 12000 \] \[ 50x = 2000 \] 
Step 3: Solve for \( x \): \[ x = \frac{2000}{50} = 40 \] Thus, the number of prizes of Rs. 100 is 40.