$A$ number is increased by $84$,it becomes $107 \%$ of itself. What is the number?

For admission in a postgraduate program of Calcutta University,$90 \%$ of the candidates who appeared for the written test were males and the rest were females. $60 \%$ of the males and $80 \%$ of the females passed the written test. What is the total number of students who appeared for the written test,if the total number of passed candidates was $1240$?

In measuring the sides of a rectangle,one side is taken $10 \%$ in excess and the other $20 \%$ in deficit. Find the error per cent in area calculated from the measurement.

In a fraction,the numerator is increased by $25 \%$ and the denominator is diminished by $10 \%$. The new fraction obtained is $\frac{5}{9}$. The original fraction is:

If $x$ is $90 \%$ of $y,$ then what per cent of $x$ is $y$?

$A$ man spends $15 \%$ of his income. If his expenditure is $Rs$ $75,$ his income (in rupees) is: