A merchant buys $200$ kg of rice at Rs. $1.25$ per kg, $400$ kg of wheat at $75$ paise per kg and $300$ kg of Jwar at $50$ paise per kg. He sells $100$ kg of rice at a loss of $25\%$. $100$ kg of wheat at a profit of $25\%$ and $100$ kg of Jawar at a profit of $30\%$. He then mixes the rest and sells $\dfrac {1}{3}$ of the mixture at $1$ rupee per kg. At what rate he should sell the remaining mixture so that he earn a profit of $25\%$ on the whole outlay?

First calculate the total cost outlay, which is 200 kg of rice at Rs. 1.25 plus 400 kg of wheat at Rs. 0.75 plus 300 kg of Jwar at Rs. 0.50, equaling Rs. 250 plus Rs. 300 plus Rs. 150, for a total outlay of Rs. 700. The target revenue to achieve a 25 percent profit is Rs. 700 multiplied by 1.25, equaling Rs. 875. After selling the initial 300 kg at their respective individual profits, the revenue generated is Rs. 93.75 plus Rs. 93.75 plus Rs. 65, which totals Rs. 252.50, leaving a remaining target of Rs. 622.50 to be earned from the final 600 kg of the mixed grain. Selling 200 kg of this mixture at Rs. 1 per kg generates Rs. 200, so the final 400 kg must be sold for Rs. 422.50, meaning the required selling rate is Rs. 1.06 per kg.

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