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

The number of coins collected per week by two coin-collectors $A$ and $B$ are In the ratio $3:4$. If the total number of coins collected by $A$ in $5$ weeks is a multiple of $7$, and the total number of coins collected by $B$ in $3$ weeks is a multiple of $24$, then the minimum possible number of coins collected by $A$ in one week is

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