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:

In mixture problems involving profit, use assumed weights based on cost data to match the required profit percentage. Compare cost price and selling price for total quantity.

Answer 1

The Correct Option is A

Given:
\[ \text{Cost of 5 kg of variety P} = ₹800 \Rightarrow \text{Cost per kg} = ₹160 \]
\[ \text{Cost of 4 kg of variety Q} = ₹800 \Rightarrow \text{Cost per kg} = ₹200 \]

Let the seller mix 5 kg of P and 4 kg of Q (to match the quantity from the cost data).
\[ \text{Total cost} = ₹800 + ₹800 = ₹1600 \]
\[ \text{Total weight} = 5 + 4 = 9\ \text{kg} \]
\[ \text{Selling price per kg} = ₹192 \Rightarrow \text{Total selling price} = 9 \times 192 = ₹1728 \]

\[ \text{Profit} = ₹1728 - ₹1600 = ₹128 \]
\[ \text{Profit \%} = \frac{128}{1600} \times 100 = 8\% \]

Thus, the assumed mixture gives exactly 8% profit, which matches the condition. Therefore, the weight ratio P : Q is:
\[ 5 : 4 \]