$A$ money lender claims to lend money at the rate of $10 \%$ per annum simple interest. However,he takes the interest in advance when he lends a sum for one year. At what interest rate does he lend the money actually?

Manish borrowed a sum of $Rs. 1150$ from Anil at the simple rate of $6$ $p.c.p.a.$ for $3$ years. He then added some more money to the borrowed sum and lent it to Sunil for the same time at $9$ $p.c.p.a.$ at simple interest. If Manish gains $Rs. 274.95$ by way of interest on borrowed sum as well as his own amount from the whole transaction,then what is the sum (in $Rs.$) lent by him to Sunil?

$A$ certain sum is invested for $T$ years. It amounts to ₹ $400$ at $10 \%$ $p.a.$. But,when invested at $4 \%$ $p.a.$,it amounts to ₹ $200$. Find the time (in years) $(T)$.

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 $Rs.$)?

$A$ 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:

If simple interest on a certain sum of money for $4$ years at $5 \%$ $p.a.$ is same as the simple interest on ₹ $560$ for $10$ years at the rate of $4 \%$ $p.a.$,then the sum of money (in ₹) is