CAT (QA) PYQs

Let a and b be natural number. If $a^2 + ab + a = 14$ and $b^2 + ab + b = 28$, then $(2a + b)$ equals

A shop owner bought a total of $64$ shirts from a wholesale market that came in two sizes, small and large. The price of a small shirt was INR $50$ less than that of a large shirt. She paid a total of INR $5000$ for the large shirts, and a total of INR $1800$ for the small shirts. Then, the price of a large shirt and a small shirt together, in INR, 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