Question

# Anandi and Rutuja invested $Rs.10,000$ each in a business. Anandi withdrew her capital after 7 months. Rutuja continued for the year. After one year, the profit earned by them was $Rs.5,700$.Find the profit earned by each person.

Hint: The above problem is a general problem with quantitative relation between two amounts. It could be solved using the concept of ratios.

It is given in the problem that Anandi and Rutuja invested $Rs.10,000$ each in a business.
Also, Anandi invested for $7$ months while Rutuja for $12$ months.
Their Combined profit is equal to $Rs.5,700$.
Since the principal amount of investment is the same for both, hence individual profit should depend upon the ratio of time period of the investments.
Therefore, we need to find the ratio of their time periods of the investment.
Ratio of time period of investment of Anandi to Rutuja is equal to $7:12$.
$\Rightarrow$ The profit earned by them is divided in the ratio of $7:12$
In order to find the individual profit, we will use the expression
Individual Profit $= \dfrac{{\Pr oportion{\text{ }}in{\text{ }}ratio}}{{Sum{\text{ }}of{\text{ }}ratio}} \times Total{\text{ }}profit$
We have $Sum{\text{ }}of{\text{ }}ratio = 7 + 12 = 19$.
And $Total{\text{ }}profit = 5700$.
Using in the above-mentioned formula,
$\Rightarrow$Anandi’s Profit $= \dfrac{7}{{19}} \times 5700 = 2100$
$\Rightarrow$Rutuja’s Profit $= \dfrac{{12}}{{19}} \times 5700 = 3600$
Hence Anandi’s individual profit is $Rs.2,100$ while Rutuja’s individual profit is $Rs.3,600$.

Note: A ratio between two or more quantities is a way of measuring their sizes compared to each other. The above method is used to solve problems in which the method of division is easy. It is important to understand the language of problems in order to divide into correct ratios. Also, units should be verified while determining the ratios as they should be the same.