Discussion
A shopkeeper mixes 20 kg of wheat at ₹24 per kg with 30 kg at ₹18 per kg. What is the price of the mixture per kg?
Answer: A
Correct answer: ₹20.40
The price of a mixture is the total cost divided by the total quantity - a weighted average rather than a simple one. The total cost is \[ 20 \times 24 + 30 \times 18 = 480 + 540 = 1020, \] and the total quantity is 50 kg, so \[ \text{price} = \frac{1020}{50} = 20.40 \text{ per kg}. \] The distractor 21 is the simple average of 24 and 18, which would be correct only if equal quantities were mixed. Because more of the cheaper wheat is used, the mixture price must lie below the midpoint - and noticing that rules out both 21 and 22 at once. This is the direct problem; alligation solves the inverse one, finding the ratio when the mixture price is given. The two are the same relation read in opposite directions, and it is worth being able to move either way: \[ \text{mean} = \frac{q_{1}p_{1} + q_{2}p_{2}}{q_{1} + q_{2}}. \]
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