$A$ money lender finds that due to a fall in the annual rate of interest from $8 \%$ to $7 \frac{3}{4} \%,$ his yearly income diminishes by ₹ $61.50$. His capital (in ₹) is:

Arun gives his wife Asha a birthday gift,giving her each year a number of rupees equal to the number of years of her age. If her birthday falls on $August \, 8$,what sum must be placed at simple interest at $7 \%$ on $January \, 1$,before she is $42$,in order to raise the required sum (in $Rs.$)?

Sumit lent some money to Mohit at $5 \%$ $p.a.$ simple interest. Mohit lent the entire amount to Birju on the same day at $8 \frac{1}{2} \%$ $p.a.$ In this transaction,after a year Mohit earned a profit of ₹ $350.$ Find out the sum of money (in ₹) lent by Sumit to Mohit.

With a given rate of simple interest,the ratio of principal and amount for a certain period of time is $4:5$. After $3$ years,with the same rate of interest,the ratio of the principal and amount becomes $5:7$. The rate of interest per annum is (in $\%$):

If ₹ $1000$ is invested at an interest rate of $5 \%$ and the interest is added to the principal every $10$ years,then the number of years in which it will amount to ₹ $2000$ is:

$A$ sum of money doubles itself in $8$ years. In how many years will it treble?