CAT (QA) PYQs

In a village, the ratio of number of males to females is $5: 4$. The ratio of number of literate males to literate females is $2 : 3$. The ratio of the number of illiterate males to illiterate females is $4: 3$. If $3600$ males in the village are literate, then the total number of females in the village 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 scores of Amal and Bimal in an examination are in the ratio $11:14$. After an appeal, their scores increase by the same amount and their new scores are in the ratio $47 : 56$. The ratio of Bimal's new score to that of his original score is