CAT (QA) PYQs

A donation box can receive only cheques of Rs. $100$, Rs. $250$, and Rs. $500$. On one good day, the donation box was found to contain exactly $100$ cheques amounting to a total sum of Rs. $15250$. Then, the maximum possible number of cheques of Rs. $500$ that the donation box may have contained, is

Let $A, B$ and $C$ be three positive integers such that the sum of $A$ and the mean of $B$ and $C$ is $5.$ In addition, the sum of $B$ and the mean of $A$ and $C$ is $7.$ Then the sum of $A$ and $B$ is

A shop wants to sell a certain quantity (in kg) of grains. It sells half the quantity and an additional 3 kg of these grains to the first customer. Then, it sells half of the remaining quantity and an additional 3 kg of these grains to the second customer. Finally, when the shop sells half of the remaining quantity and an additional 3 kg of these grains to the third customer, there are no grains left. The initial quantity, in kg, of grains is