$A$ person's present age is two-fifth of the age of his mother. After $8$ years,he will be one-half of the age of his mother. How old is the mother at present (in $years$)?

If $A$ and $B$ are in the ratio $4:5$ and the difference of their squares is $81,$ what is the value of $A?$

The ratio of the incomes of $A$ and $B$ is $5:4$ and the ratio of their expenditures is $3:2$. If at the end of the year,each saves $Rs. 1600$,then the income of $A$ is (in $Rs.$):

Find the fraction which bears the same ratio to $\frac{1}{27}$ that $\frac{3}{7}$ does to $\frac{5}{9}$.

$A$ man divides his property such that his son's share to his wife's share and his wife's share to his daughter's share are both in the ratio $3:1$. If the daughter gets ₹ $10,000$ less than the son,what is the total value of the property in ₹?

The annual incomes and expenditures of a man and his wife are in the ratios of $5: 3$ and $3: 1$,respectively. If they decide to save equally and find a balance of ₹ $4000$ at the end of the year (total savings),their incomes were: