Anil bought an item with $12 \frac{1}{2} \%$ discount on the labelled price. He sold the item with $17 \frac{1}{2} \%$ profit on the labelled price. What was his percent profit on the price he bought?

$A$ shopkeeper has to sell $24 \text{ kg}$ of sugar. He sells a part of these at a gain of $20 \%$ and the rest at a loss of $5 \%$. If on the whole he earns a profit of $10 \%$,what is the quantity of sugar (in $\text{kg}$) sold at a loss?

Nutan pays $Rs. 2140$ for $3$ calculators and $4$ pens,while she pays $Rs. 1355$ for $1$ additional calculator and $5$ pens. What is the cost of a calculator in $Rs.$?

$A$ trader mixes $26 \text{ kg}$ of rice at $Rs. 20$ per $\text{kg}$ with $30 \text{ kg}$ of rice of another variety at $Rs. 36$ per $\text{kg}$ and sells the mixture at $Rs. 30$ per $\text{kg}$. His profit percent is:

$A$ shopkeeper gains the cost of $8$ metres of thread by selling $40$ metres of thread. Find his gain percent.

$A$ shopkeeper marks his goods at $40 \%$ above their cost price. He is able to sell $\frac{3}{4}$ of his goods at this price,and the remaining at $40 \%$ discount. Assuming that the shopkeeper is able to sell all the goods he buys,find his overall gain or loss percentage.