Discussion
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)?
Answer: A
The ratio is 5:4.
Variety P costs 800/5 = ₹ 160 per kg and variety Q costs 800/4 = ₹ 200 per kg. Selling at ₹ 192 with 8% profit means the cost price of the mixture is:
\[ \frac{192}{1.08} = 177.78\ \text{per kg} = \frac{1600}{9} \]
By alligation:
\[ \begin{aligned} \frac{P}{Q} &= \frac{200-177.78}{177.78-160} \\ &= \frac{22.22}{17.78} = \frac{5}{4} \end{aligned} \]
Check: 5 kg of P and 4 kg of Q cost 800 + 800 = ₹ 1600 for 9 kg, and selling 9 kg at 192 gives ₹ 1728, exactly 8% more. 1:1 would give a cost of ₹ 180 per kg and only 6.7% profit.
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