CAT (QA) PYQs

The price of a precious stone is directly proportional to the square of its weight. Sita has a precious stone weighing $18$ units. If she breaks it into four pieces with each piece having distinct integer weight, then the difference between the highest and lowest possible values of the total price of the four pieces will be $288000$. Then, the price of the original precious stone is

In September, the incomes of Kamal, Amal and Vimal are in the ratio $8 : 6 : 5$. They rent a house together, and Kamal pays $15\%$, Amal pays $12\%$ and Vimal pays $18\%$ of their respective incomes to cover the total house rent in that month. In October, the house rent remains unchanged while their incomes increase by $10\%$, $12\%$ and $15\%$, respectively. In October, the percentage of their total income that will be paid as house rent, is nearest to

The scores of Amal and Bimal in an examination are in the ratio $11:14$. After an appeal, their scores increase by the same amount and their new scores are in the ratio $47 : 56$. The ratio of Bimal's new score to that of his original score is