Question

If a product is created with subproducts A and B in the ratio 1:1, then its cost is INR 500 per unit. If it is created with subproducts A and B in the ratio 3:1, then its cost is INR 300 per unit. What are the costs per unit (in INR) of subproducts A and B respectively?

• A. 900, 100
• B. 300, 700
• C. 700, 300
• D. 100, 900

Hint:

For mixture problems, convert ratios into weighted average equations to easily form and solve linear equations.

Answer 1

The Correct Option is D

Step 1: Assume the costs of subproducts.
Let the cost per unit of subproduct A be \( x \) INR.
Let the cost per unit of subproduct B be \( y \) INR.
Step 2: Form equation from the first condition.
When A and B are mixed in the ratio \( 1:1 \), the average cost per unit is 500 INR.
\[ \frac{x + y}{2} = 500 \]
\[ x + y = 1000 \]
Step 3: Form equation from the second condition.
When A and B are mixed in the ratio \( 3:1 \), the average cost per unit is 300 INR.
\[ \frac{3x + y}{4} = 300 \]
\[ 3x + y = 1200 \]
Step 4: Solve the system of equations.
Subtracting equation (1) from equation (2):
\[ (3x + y) - (x + y) = 1200 - 1000 \]
\[ 2x = 200 \]
\[ x = 100 \]
Step 5: Find the value of \( y \).
Substitute \( x = 100 \) in \( x + y = 1000 \):
\[ 100 + y = 1000 \]
\[ y = 900 \]
Step 6: Conclusion.
The cost per unit of subproduct A is 100 INR and subproduct B is 900 INR.