Mohit purchased $40 \, kg$ of wheat at $Rs. 12.50$ per $kg$ and $25 \, kg$ of wheat at $Rs. 15.10$ per $kg$. He mixed the two qualities of wheat for selling. At what rate should it be sold to gain $10 \%$? (in $Rs.$)

$A$ fruit seller sells $\frac{3}{5}$ th part of fruit at a profit of $10 \%$ and the remaining at a loss of $5 \%$. If the total profit is $Rs. 1500$,then what is the total cost price of the fruit in $Rs.$?

$A$ dealer buys an article listed at $Rs. 100$ and gets successive discounts of $10\%$ and $20\%$. He spends $10\%$ of the cost price on transportation. At what price should he sell the article to earn a profit of $15\%$? (in $Rs.$)

$A$ trader buys goods at a $20 \%$ discount on the marked price. If he wants to make a profit of $25 \%$ after allowing a discount of $20 \%$ on his new marked price,by what percent should his new marked price be greater than the original marked price?

Ram sells an article to Girish at a gain of $20 \%$,Girish sells it to Sanjay at a gain of $10 \%$,and Sanjay sells it to Aditya at a gain of $12 \frac{1}{2} \%$. If Aditya pays $Rs. 59.40$,what did it cost Ram in $Rs.$?

$P$ 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 $Rs.$)