The profit earned by selling an article for $Rs. 900$ is double the loss incurred when the same article is sold for $Rs. 450$. At what price should the article be sold to make $25\%$ profit?

Nisha bought a number of oranges at $2$ for a rupee and an equal number at $3$ for a rupee. To make a profit of $20 \%$ she should sell a dozen for (in $Rs.$)

Sasha goes to a shop to buy a sofa set and a center table. She bargains for a $10 \%$ discount on the center table and a $25 \%$ discount on the sofa set. However,the manager,by mistake,interchanged the discount percentage figures while making the bill and Sasha paid accordingly. When compared to what she should have paid for her purchases,what percentage did Sasha pay extra,given that the center table costs $40 \%$ as much as the sofa set (in $\%$)?

$P$ invests $Rs. 9100$ for $3$ months. $Q$ invests $Rs. 6825$ for $2$ months and $R$ invests $Rs. 8190$ for $5$ months in a business. If the total profit amounts to $Rs. 4158$,how much profit should $Q$ get? (in $Rs.$)

Hemant purchased $120$ rims of paper at $Rs. 80$ per rim. He spent $Rs. 280$ on transportation,paid octroi at the rate of $40$ paise per rim,and paid $Rs. 72$ to the coolie. If he wants to have a gain of $8 \%$,the selling price per rim must be (in $Rs.$)

An article is sold for $Rs. 4950$ at a gain of $10 \%$. What would have been the gain or loss per cent if it had been sold for $Rs. 4275$?