A merchant buys $1260$ kg of corn $\displaystyle \frac{1}{4}$ of which he sells at a gain of $5\%$, $\displaystyle \frac{1}{3}$ at a gain of $\%$ and the remainder at a gain of $12\%$. If he had sold the whole at a gain of $10\%$ he would have gained Rs $27.30$ more. Find the cost price per kg.

Assume the missing profit percentage in the question is 4%, since selling 1/4 at 5%, 1/3 at 4%, and 5/12 at 12% results in a weighted average profit of exactly 8%. Selling everything at a 10% profit instead of an 8% profit creates an extra 2% gain on the total cost. Since 2% of the total cost equals 27.30 rupees, the total cost is 1365 rupees. Dividing this total by 1260 kg gives a cost price of 2 rupees per kg.

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