CAT 2021 Slot 3 QA Previous Year Questions with Detailed Solution

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

Anil can paint a house in \(12\) days while Barun can paint it in \(16\) days. Anil, Barun, and Chandu undertake to paint the house for ₹ \(24000\) and the three of them together complete the painting in \(6\) days. If Chandu is paid in proportion to the work done by him, then the amount in INR received by him is

Mira and Amal walk along a circular track, starting from the same point at the same time. If they walk in the same direction, then in \(45\) minutes, Amal completes exactly \(3\) more rounds than Mira. If they walk in opposite directions, then they meet for the first time exactly after \(3\) minutes. The number of rounds Mira walks in one hour is

A four-digit number is formed by using only the digits \(1, 2\) and \(3\) such that both \(2\) and \(3\) appear at least once. The number of all such four-digit numbers is

In a triangle \(ABC\), \(\angle BCA = 50^\circ\). \(D\) and \(E\) are points on \(AB\) and \(AC\), respectively, such that \(AD = DE\). If \(F\) is a point on \(BC\) such that \(BD = DF\), then \(\angle FDE\), in degrees, is equal to

For a real number \(a\), if \(\dfrac{\log_{15} a + \log_{32} a}{(\log_{15} a)(\log_{32} a)} = 4\), then \(a\) must lie in the range

The arithmetic mean of scores of \(25\) students in an examination is \(50\). Five of these students top the examination with the same score. If the scores of the other students are distinct integers with the lowest being \(30\), then the maximum possible score of the toppers is

One part of a hostel's monthly expenses is fixed, and the other part is proportional to the number of its boarders. The hostel collects ₹ \(1600\) per month from each boarder. When the number of boarders is \(50\), the profit of the hostel is ₹ \(200\) per boarder, and when the number of boarders is \(75\), the profit of the hostel is ₹ \(250\) per boarder. When the number of boarders is \(80\), the total profit of the hostel, in INR, will be

One day, Rahul started a work at \(9\) AM and Gautam joined him two hours later. They then worked together and completed the work at \(5\) PM the same day. If both had started at \(9\) AM and worked together, the work would have been completed \(30\) minutes earlier. Working alone, the time Rahul would have taken, in hours, to complete the work is

The total of male and female populations in a city increased by \(25\%\) from \(1970\) to \(1980\). During the same period, the male population increased by \(40\%\) while the female population increased by \(20\%\). From \(1980\) to \(1990\), the female population increased by \(25\%\). In \(1990\), if the female population is twice the male population, then the percentage increase in the total of male and female populations in the city from \(1970\) to \(1990\) is