Question

Ramesh started a business by investing Rs.25000. 3 months later Mahesh joined the business by investing Rs.25000. At the end of the year, Ramesh got Rs.1000 more than Mahesh out of the profit. Find the total profit

Answer 1

Hint: To solve this problem, we should know the relation between the amount of profit given to a partner and the parameters of investment like the capital that he invests and the time period for which he invests. We know that the profit given to a person is directly proportional to the amount of investment done by him. Likewise, the profit given to a person is directly proportional to the time period for which he does the investment. From the problem, we can infer that the amount of investment done by Mahesh and Ramesh are the same. But, we can infer that Ramesh has done the investment for 12 months whereas Mahesh has done it for a period of 9 months. As the profits distributed are directly proportional to the time of investment, we can write that the ratio of the profits is equal to the ratio of the time periods. So,
\[\text{Profi}{{\text{t}}_{\text{Ramesh}}}:\text{Profi}{{\text{t}}_{\text{Mahesh}}}=12:9=12x:9x\]. We can infer that the difference between both the profits is 1000 which is equal to three times x. The total profit is equal to $12x+9x=21x=7\times 3x$. Using this relation, we can find the total profit.

Complete step-by-step answer:
As mentioned in the question, we have to find the total profit which is earned by the business.
The main observation is that the profit given to a person is directly proportional to both the amount and the time period for which he has invested. Using this fact, we can write that
$\begin{align}
  & \text{Profit}\propto \text{Amount} \\
 & \text{Profit}\propto \text{Time} \\
\end{align}$
By multiplying the above equations and by removing the proportionality using a constant x, we get
$\text{Profit}=\text{Amount}\times \text{Time}\times x$
In our question, Ramesh has invested Rs.25000 for 12 months and Mahesh has invested Rs.25000 for 9 months. We can write their profits as
$\begin{align}
  & \text{Profi}{{\text{t}}_{\text{Ramesh}}}=25000\times 12\times x \\
 & \text{Profi}{{\text{t}}_{\text{Mahesh}}}=25000\times 9\times x \\
\end{align}$
The total profit is the sum of their profits
Total profit $=25000\times 12\times x+25000\times 9\times x=21\times \left( 25000x \right)\to \left( 1 \right)$
We can see from the question that the difference of profits is Rs.1000. We can write that
$\begin{align}
  & 25000\times 12\times x-25000\times 9\times x=1000 \\
 & 3\left( 25000x \right)=1000\to \left( 2 \right) \\
\end{align}$
We can write the equation-1 as
Total profit $=7\times 3\times \left( 25000x \right)$
Using the equation-2 in above equation, we get
Total profit $=7\times 1000=\text{Rs}.7000$
$\therefore $ The total profit earned by both Ramesh and Mahesh is Rs.7000.

Note: Students can be confused to solve the question if the two parameters which are the amount and the time are varying. In our question, the amounts invested are the same and they actually cancel out in the whole calculations. If the amounts are different, we can use the main logic behind the solution which is the proportionality relation between the profit and the parameters.