Two successive discounts of $a \%$ and $b \%$ on the marked price of an article are equivalent to a single discount of:

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 $Rs.$)

The marked price of an item is $Rs. 900$. On the purchase of $2$ items,the discount is $16\%$,and on the purchase of $5$ items,the discount is $44\%$. If Raksha buys $7$ items,what is the effective discount percentage?

$A$ man bought a watch for $10 \%$ discount. If he had bought it for $20 \%$ discount,he would have saved $Rs.\, 125$ more. The marked price of the watch is (in $Rs.$):

$A$ bill is discounted at $5 \%$ per annum. If banker's discount be allowed, at what rate of interest must the proceeds be invested, so that nothing is lost? (in $\%$)

$A$ retailer marks up his goods by $150 \%$ and offers a $40 \%$ discount. What will be the selling price (in $Rs.$) if the cost price is $Rs.\, 800$?