CAT (QA) PYQs

Suppose, $C1, C2, C3, C4,$ and $C5$ are five companies. The profits made by $C1, C2,$ and $C3$ are in the ratio $9: 10: 8$ while the profits made by $C2, C4,$ and $C5$ are in the ratio $18:19:20$. If $C5$ has made a profit of Rs $19$ crore more than $C1$, then the total profit (in Rs) made by all five companies is

If $a$ and $b$ are integers of opposite signs such that $(a+3)^{2}: b^{2}=9: 1$ and $(a-1)^{2}:(b-1)^{2}=4: 1$, then the ratio $a^{2}: b^{2}$ is

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