CAT (QA) PYQs

If a certain weight of an alloy of silver and copper is mixed with $3$ kg of pure silver, the resulting alloy will have $90\%$ silver by weight. If the same weight of the initial alloy is mixed with $2$ kg of another alloy which has $90\%$ silver by weight, the resulting alloy will have $84\%$ silver by weight. Then, the weight of the initial alloy, in kg, is

A container has $40$ liters of milk. Then, $4$ liters are removed from the container and replaced with $4$ liters of water. This process of replacing $4$ liters of the liquid in the container with an equal volume of water is continued repeatedly. The smallest number of times of doing this process, after which the volume of milk in the container becomes less than that of water, is

From a container filled with milk, $9$ litres of milk are drawn and replaced with water. Next, from the same container, $9$ litres are drawn and again replaced with water. If the volumes of milk and water in the container are now in the ratio of $16: 9$, then the capacity of the container, in litres, is