The banker's gain on a certain sum of money due for $9$ months at $4 \%$ $p.a.$ is $Rs. 2.25$. The sum is (in $Rs.$)

$A$ dealer marks a washing machine for $Rs.\, 7500$ and allows a discount of $6 \%$ on it. Find its selling price in $Rs.$

$A$ cloth merchant has announced a $25 \%$ rebate in prices. If one needs to have a rebate of $Rs. 40$,then how many metres of cloth costing $Rs. 32$ per metre should he purchase?

At a given rate,the simple interest and the true discount on a certain sum,for a given time,are $Rs. 24$ and $Rs. 22$ respectively. The sum is (in $Rs.$)

When a discount of $Rs. 42$ is allowed on the marked price of an article,the new reduced price becomes $86 \%$ of the original marked price. Find the marked price (in $Rs.$).

$A$ owes $B$ $Rs. 1350$ due in $3$ months and $B$ owes $A$ $Rs. 1078$ due in $5$ months. If they agree to settle their account right now at $5\%$ $p.a.$ simple interest,how much should $A$ pay to $B$ (in $Rs.$)?