$A$ shopkeeper purchased $70$ $kg$ of potatoes for $Rs. 420$ and sold the whole lot at the rate of $Rs. 6.5$ per $kg$. What will be his gain percent?

Two items $A$ and $B$ are sold at a profit of $10 \%$ and $15 \%,$ respectively. If the amount of profit received is the same,then the cost price of $A$ and $B$ may be (in $Rs.$)

At a cost of $60$ paise per article,Sarika produces $750$ articles. She sets the selling price such that if only $600$ articles are sold,she would have made a profit of $40 \%$ on the total outlay. However,$120$ articles got spoilt and she was able to sell $630$ articles at this price. Find her actual profit or loss percent as a percentage of the total outlay,assuming that the unsold articles are useless.

$A$ trader sold an article at a gain of $20 \%$. Had he purchased it for $40 \%$ more and sold for $Rs. 24$ less,he would have incurred a loss of $20 \%$. What is the cost price (in $Rs.$) of the article?

$A$ shopkeeper professes to sell his goods at cost price but uses a $930 \text{ g}$ weight instead of $1 \text{ kg}$ weight. What will be the profit percentage of the shopkeeper (in $\%$)?

$A$ fair price shopkeeper takes $10 \%$ profit on his goods. He lost $20 \%$ of his goods due to theft. What is his loss percentage (in $\%$)?