$Rs.\, 20$ is the true discount on $Rs.\, 210$ due after a certain time. What will be the true discount on the same sum due after half of the former time,the rate of interest being the same? (in $Rs.$)

$A$ sells a car priced at $Rs. 36,000$. He gives a discount of $8\%$ on the first $Rs. 20,000$ and $5\%$ on the remaining $Rs. 16,000$. $B$ also sells a car of the same make,priced at $Rs. 36,000$. He gives a discount of $7\%$ on the total price. Calculate the actual prices charged by $A$ and $B$ for the cars (in $Rs.$).

If two successive discounts of $50 \%$ and $10 \%$ are offered,what is the net discount (in $\%$) ?

Ramesh marks his goods $30 \%$ above cost price. If he sells the item for $Rs. 910$ after allowing a discount of $15 \%$,find his cost 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?

$A$ has to pay $Rs. 220$ to $B$ after $1$ year. $B$ asks $A$ to pay $Rs. 110$ in cash and defers the payment of the remaining $Rs. 110$ for $2$ years. $A$ agrees to it. Counting the rate of interest at $10\%$ per annum in this new mode of payment,which of the following is true?