Question

A trader sells 10 litres of a mixture of paints A and B, where the amount of B in the mixture does not exceed that of A.The cost of paint A per litre is Rs. 8 more than that of paint B. If the trader sells the entire mixture for Rs. 264 and makes a profit of 10%, then the highest possible cost of paint B, in Rs. per litre, is

• A. 26
• B. 16
• C. 20
• D. 22

Answer 1

The Correct Option is C

Step 1: Assign variables 

Let:

• \( a \) = litres of paint A in the mixture
• \( b \) = litres of paint B in the mixture
• Cost of paint B = \( x \) per litre
• Cost of paint A = \( x + 8 \) per litre

Step 2: Selling and buying price of the mixture

Total selling price of the mixture: \[ \text{SP} = 264 \] Profit percentage: \[ 10\% \] Thus, the total cost price (CP) of the mixture is: \[ \text{CP} = \frac{264 \times 100}{110} = 240 \] The price per litre of the mixture: \[ \frac{240}{10} = 24 \ \text{per litre} \]

Step 3: Equation for total cost

The total cost is: \[ (x + 8)a + xb = 240 \]

Step 4: Condition for maximizing \( x \)

We are told: \[ b \le a \] To maximize \( x \), we minimize \( a \). If the total volume is \( 10 \) litres, the smallest integer \( a \) can be is \( 5 \), so \( b = 5 \).

Step 5: Substituting values

\[ (x + 8)(5) + x(5) = 240 \] \[ 5x + 40 + 5x = 240 \] \[ 10x + 40 = 240 \] \[ 10x = 200 \quad \Rightarrow \quad x = 20 \]

✅ Final Answer: The maximum cost of paint B is ₹20 per litre.