$A$ man invested $\frac{1}{3}$ of his capital at $7 \%$,$\frac{1}{4}$ at $8 \%$,and the remainder at $10 \%$. If the annual income is ₹ $561$,the capital (in ₹) is:

Asmita invests an amount of $Rs. 9535$ at the rate of $4\%$ per annum to obtain a total amount of $Rs. 11442$ on simple interest after a certain period. For how many years did she invest the amount to obtain the total sum?

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 becomes $Rs. 1100$ in $2$ years and $Rs. 1400$ in $6$ years at $S.I.$ Find the rate percent.

$A$ 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.

The simple interest on a sum is $\frac{1}{16}$ of the principal and the number of years is equal to the rate per cent per annum. The rate per cent per annum is (in $.5$)