CAT (QA) PYQs

A sum of money is split among Amal, Sunil and Mita so that the ratio of the shares of Amal and Sunil is $3: 2$, while the ratio of the shares of Sunil and Mita is $4: 5$. If the difference between the largest and the smallest of these three shares is Rs $400$, then Sunil's share, in rupees, 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 ratio of expenditures of Lakshmi and Meenakshi is $2:3$, and the ratio of income of Lakshmi to expenditure of Meenakshi is $6:7$. If excess of income over expenditure is saved by Lakshmi and Meenakshi, and the ratio of their savings is $4:9$, then the ratio of their incomes is