Arun lends ₹ $20,000$ to two of his friends. He gives ₹ $12,000$ to the first at $8 \%$ p.a. simple interest. Arun wants to make a profit of $10 \%$ on the whole. The simple interest rate $\%$ at which he should lend the remaining sum of money to the second friend is

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

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 $Rs.$)?

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:

David invested a certain amount in three different schemes $A, B$ and $C$ with the rate of interest $10 \% \text{ p.a.}, 12 \% \text{ p.a.}$ and $15 \% \text{ p.a.}$ respectively. If the total interest accrued in one year was ₹ $3200$ and the amount invested in scheme $C$ was $150 \%$ of the amount invested in scheme $A$ and $240 \%$ of the amount invested in scheme $B$, what was the amount (in ₹) invested in scheme $B$?

₹ $1500$ is invested at a rate of $10 \%$ simple interest,and the interest is added to the principal after every $5$ years. In how many years will it amount to ₹ $2500$?