CAT (QA) PYQs

The ratio of the number of students in the morning shift and afternoon shift of a school was 13 : 9. After 21 students moved from the morning shift to the afternoon shift, this ratio became 19 : 14. Next, some new students joined the morning and afternoon shifts in the ratio 3 : 8 and then the ratio of the number of students in the morning shift and the afternoon shift became 5 : 4. The number of new students who joined 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

In an election, there were four candidates and $80\%$ of the registered voters casted their votes. One of the candidates received $30 \%$ of the casted votes while the other three candidates received the remaining casted votes in the proportion $1: 2: 3$. If the winner of the election received $2512$ votes more than the candidate with the second highest votes, then the number of registered voters was