Question

When three different varieties of a chemical are mixed in the ratio 3 : 7 : 8, the cost price of the mixture is Rs.\ 15 per litre. However, when the same varieties are mixed in the ratio 2 : 5 : 9, the cost price of the mixture is Rs.\ 18 per litre. What is the cost price of the mixture formed (in Rs.\ per litre) when the same three varieties of chemical are mixed in the ratio 6 : 13 : 5?

• A. 12
• B. 15
• C. 9
• D. 18
• E. None of these

Hint:

In mixture problems with repeated components and different ratios, forming linear equations based on weighted averages is the fastest technique.

Answer 1

The Correct Option is C

Step 1: Find the price per litre of each chemical.
Let the prices of the three chemicals be \( x, y, z \). From the given mixtures:
Mixture 1 ratio \( 3:7:8 \) gives: \[ \frac{3x + 7y + 8z}{18} = 15 \quad \Rightarrow \quad 3x + 7y + 8z = 270 \] Mixture 2 ratio \( 2:5:9 \) gives: \[ \frac{2x + 5y + 9z}{16} = 18 \quad \Rightarrow \quad 2x + 5y + 9z = 288 \] Step 2: Subtract equations to eliminate variables.
Subtract the two equations: \[ (3x + 7y + 8z) - (2x + 5y + 9z) = 270 - 288 \] \[ x + 2y - z = -18 \] Step 3: Use weighted-average approach.
For mixture 3, ratio = \( 6:13:5 \), total = 24. Cost price of mixture 3 = \[ \frac{6x + 13y + 5z}{24} \] Using system-solving methods (eliminating variables), the value of \[ 6x + 13y + 5z = 216 \] Thus, mixture price: \[ \frac{216}{24} = 9 \] Step 4: Conclusion.
The cost price of the final mixture is Rs.\ 9 per litre.