$A$ man invests a certain sum of money at $6 \%$ $p.a.$ simple interest and another sum at $7 \%$ $p.a.$ simple interest. His income from interest after $2$ $years$ was $Rs. 354$. One-fourth of the first sum is equal to one-fifth of the second sum. Find the total sum (in $Rs.$) he invested.

Nutan borrowed some money at a rate of $4$ $p.c.p.a.$ for the first $3$ years,at the rate of $8$ $p.c.p.a.$ for the next $2$ years,and at the rate of $9$ $p.c.p.a.$ for the period beyond $5$ years. If she paid a total $SI$ of $Rs. 19550$ at the end of $7$ years,how much money (in $Rs.$) did she borrow?

If the amount obtained by Mahesh by investing ₹ $1500$ for $2 \frac{1}{2}$ years at the rate of $8 \%$ $p.a.$ is equal to the amount obtained by Suresh by investing a certain sum for $2$ years at $5 \%$ $p.a.$ simple interest,then the sum invested by Suresh is

According to a census report,the population growth rate of Faridabad is going to be an increasing $A.P.$ with the first year's rate as $5 \%$ and common difference as $5 \%$,but simultaneously the migration rate is an increasing $G.P.$ with the first term as $1 \%$ and common ratio of $2$. If the population on $31 \, \text{December}, 2010$ is $1 \, \text{million}$,then find in which year will Faridabad witness its first fall in population?

$A$ sum of money becomes $\frac{8}{5}$ of itself in $5$ $years$ at a certain rate of interest. The rate per cent per annum is

$A$ person receives a simple interest of ₹ $1,000$ on a certain principal at the rate of $5 \%$ $p.a.$ in $4$ years. What compound interest (in ₹) will that person receive on twice the principal in $2$ years at the same rate?