Question

A business person buys potatoes of two different varieties \(P\) and \(Q\), mixes them in a certain ratio and sells them at ₹ 192 per kg. The cost of the variety \(P\) is ₹ 800 for 5 kg.
The cost of the variety \(Q\) is ₹ 800 for 4 kg.
If the person gets 8% profit, what is the \(P:Q\) ratio (by weight)?

• A. 5:4
• B. 3:4
• C. 3:2
• D. 1:1

Hint:

For profit-based mixture problems, always back-calculate the cost price using \(\text{CP} = \frac{\text{SP}}{1+\text{Profit%}}\), then apply the weighted average rule.

Answer 1

The Correct Option is A

Step 1: Calculate cost per kg.
For variety \(P\): \[ \frac{800}{5} = ₹ 160 \ \text{per kg} \] For variety \(Q\): \[ \frac{800}{4} = ₹ 200 \ \text{per kg} \]

Step 2: Effective cost price of mixture.
Selling price = ₹ 192 with 8% profit.
So, \[ \text{CP of mixture} = \frac{192}{1.08} = ₹ \frac{1600}{9} \approx ₹ 177.78 \]

Step 3: Use weighted average.
Let the ratio be \(P:Q = x:y\). Then, \[ \frac{160x + 200y}{x+y} = \frac{1600}{9} \] Multiply across: \[ 9(160x + 200y) = 1600(x+y) \] \[ 1440x + 1800y = 1600x + 1600y \] \[ 160x = 200y \Rightarrow \frac{x}{y} = \frac{5}{4} \]

Step 4: Conclusion.
Thus, the required ratio is \[ P:Q = 5:4 \] Final Answer: \[ \boxed{5:4} \]