CAT (QA) PYQs

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

In an examination, Rama's score was one-twelfth of the sum of the scores of Mohan and Anjali. After a review, the score of each of them increased by $6$. The revised scores of Anjali, Mohan, and Rama were in the ratio $11:10:3$. Then Anjali's score exceeded Rama's score by

Anil, Bobby and Chintu jointly invest in a business and agree to share the overall profit in proportion to their investments. Anil's share of investment is $70\%$. His share of profit decreases by Rs. $420$ if the overall profit goes down from $18\%$ to $15\%$. Chintu's share of profit increases by Rs. $80$ if the overall profit goes up from $15\%$ to $17\%$. The amount, in INR, invested by Bobby is