Profit and Loss. A person has 100 kg sugar. some of it he sold at 7% profit and remaining  sold at at 17% profit.total profit he got was 10%. Then how much of kg he sold at 17% profit?
 A: Suppose $x$ kg. was sold at $7\%$ profit. It follows that $100-x$ kg. was sold at $17\%$ profit. Can you find the total profit percentage expressed in $x$?
A: Assume that the per kilogram price is $A$. That is, the merchant paid $100A$ Rupees for the sugar. 
If the merchant sells the sugar for $B$ Rupees and if the profit profit is $10\%$ then
$$B=100A\times1.10$$
How much is $B$? If the merchant made $17\%$ profit on $x$ kilograms of sugar and $7\%$ profit on $100-x$ kilograms of sugar then
$$B=xA\times 1.17+(100-x)A\times1.07.$$That is, we have the following equation
$$100A\times 1.10=xA\times 1.17+(100-x)\times 1.07.$$
$A$ cancels out and we have $$110=x1.17+107-x1.07$$
or $$3=x0.1.$$
So, $$x=\frac3{0.1}=30 [kg].$$
A: $x$ kg. we get $7\%$ profit, $100-x$ we get $17\%$ profit and for the entire $100$ kg. we get $10\%$ profit.
hence for $x$ kg. we get $x+\frac{7x}{100}$ and for $(100-x)$ kg. we get $100-x+\frac{17\cdot(100-x)}{100}$ and for $100$ kg. we get $100+\frac{10}{100}$
Combine in equation
$$x+\frac{7x}{100}+100-x+\frac{17\cdot(100-x)}{100}=110$$
Solve for $x$ and the solution is $30$.
A: $x + y = 100$.........(1)
$1.07x + 1.17y = 110$........(2)
Multiply equation (1) by $1.07$
Subtract the new equation (1) from equation (2) to eliminate the x variable and solve for y for the quantity sold at $17\%$ profit.
