The value of an article depreciates every year at the rate of $10 \%$ of its value. If the present value of the article is $Rs.\, 729$, then its worth $3\, years$ ago was (in $Rs.$)

A shopkeeper bought $30\, Kg$ of wheat at the rate of $Rs.\,45$ per $Kg.$ He sold $40\%$ of the total quantity at the rate of $Rs.\,50$ per $Kg.$ Approximately, at what price per $Kg$ should he sell the remaining quantity to make $25$ percent overall profit? (in $Rs.$)

$A, B, C$ are partners in a business. During a particular $year,$ A received one third of the profit, $B$ received $\frac{1}{4}$ of the profit and $C$ received the remaining $Rs.\, 5000$ How much amount of money did A receive? (in $Rs.$)

A sells an article to $B$ at a gain of $20 \%$ and $B$ sells it to $C$ at a gain of $10 \%$ and $C$ sells it to $D$ at a gain of $12 \frac{1}{2} \% .$ If $D$ pays $Rs.\, 29.70,$ then $A$ purchased the article for (in $Rs.$)

A sells his house worth $Rs.\, 10\, lakh$ to $B$ at a loss of $10 \% .$ Later $B$ sells it back to $A$ at $10 \%$ profit. The result of the two transactions is