Question

A invested Rs. 25,300 for 7 months, B invested Rs. 25,200 for 11 months and C invested Rs. 27,500 for 7 months. Find the share of A and C together out of a total profit of Rs. 33,600.

Hint – Total investment of each person is respective months multiplied by respective investment. Share of profit earned by A and C is corresponding to their investment .(Use properties of ratio).

Given data
A invested Rs. 25,300 for 7 months.
Therefore total investment of A $= \left( {25300 \times 7} \right)$
B invested Rs. 25,200 for 11 months.
Therefore total investment of B $= \left( {25200 \times 11} \right)$
C invested Rs. 27,500 for 7 months.
Therefore total investment of C $= \left( {27500 \times 7} \right)$
Therefore ratio of their investment are
$A:B:C = \left( {25300 \times 7} \right):\left( {25200 \times 11} \right):\left( {27500 \times 7} \right)$
Divide by 1100 we get
$\begin{gathered} A:B:C = \left( {23 \times 7} \right):\left( {252} \right):\left( {25 \times 7} \right) \\ A:B:C = 161:252:175 \\ \end{gathered}$
Now it is given that the total profit is Rs. 33,600.
Let the share of A, B and C is x, y and z respectively.
So, the share of x is
$\begin{gathered} \Rightarrow x = \dfrac{{161}}{{161 + 252 + 175}} \times 33600 \\ \Rightarrow x = \dfrac{{161}}{{588}} \times 33600 \\ \end{gathered}$
So, the share of y is
$\begin{gathered} \Rightarrow y = \dfrac{{252}}{{161 + 252 + 175}} \times 33600 \\ \Rightarrow y = \dfrac{{252}}{{588}} \times 33600 \\ \end{gathered}$
So, the share of z is
$\begin{gathered} \Rightarrow z = \dfrac{{175}}{{161 + 252 + 175}} \times 33600 \\ \Rightarrow z = \dfrac{{175}}{{588}} \times 33600 \\ \end{gathered}$
So the share of A and C together is
$\begin{gathered} x + z = \dfrac{{161}}{{588}} \times 33600 + \dfrac{{175}}{{588}} \times 33600 \\ \Rightarrow x + z = \dfrac{{336}}{{588}} \times 33600 = 19200 \\ \end{gathered}$
So, the share of A and C together out of a total profit of Rs. 33,600 is Rs. 19,200.

Note – In such types of questions first calculate the total investment of the respective persons then calculate the ratio of their investments and simplify, from this we get the percentage amount they invested, which then can be multiplied with the total profit earned to get the share of profit earned by the respective person .