$P, Q$ and $R$ invested their capital in the ratio of $8:6:5$. At the end of the business,they received the profit in the ratio of $1:3:5$. Find the ratio of time for which they contributed their capital.

$A$ and $B$ started a business in partnership investing ₹ $20000$ and ₹ $15000$ respectively. After six months,$C$ joined them with ₹ $20000$. What will be $B$'s share in the total profit of ₹ $25000$ earned at the end of $2$ years from the starting of the business? (In ₹)

$A$,$B$ and $C$ start a business. If the ratio of their periods of investments is $2: 3: 6$ and their profits are in the ratio of $4: 5: 6$, then the ratio of capitals of $A$,$B$ and $C$ is

How many statements are required to find: What is the amount invested in Scheme $B$?
$I$. The amounts invested in Schemes $A$ and $B$ are in the ratio of $2:3$.
$II$. The amount invested in Scheme $A$ is $40\%$ of the total amount invested.
$III$. The amount invested in Scheme $A$ is ₹ $45,000$.

Mahesh,Suresh,and Ganesh entered into a partnership business. Mahesh invested ₹ $16,000$ for $9 \text{ months}$. Suresh invested ₹ $12,000$ for $6 \text{ months}$,and Ganesh invested ₹ $8,000$ for $12 \text{ months}$. At the end of a year,there was a profit of ₹ $26,000$. Find out the share of Suresh in the profit (in ₹).

Two friends $P$ and $Q$ started a business investing in the ratio of $5:6$. $R$ joined them after six months investing an amount equal to that of $Q$. At the end of the year,$20\%$ profit was earned which was equal to $₹ 98000$. What was the amount invested by $R$?