Three persons start a business and spend Rs. 25,000, Rs. 15,000 and Rs. 40,000 respectively. Find the share of each out of a profit of Rs. 14,400 in a year.

Hint: It is given that three persons start a business and spend Rs. 25,000, Rs. 15,000 and Rs. 40,000 respectively. Therefore, find the ratio of their investment. Now, they must have their share in the profit in the same ratio of their investment.

Complete step-by-step answer:
It is given that three persons start a business and spend Rs. 25,000, Rs. 15,000 and Rs. 40,000 respectively.
Suppose,
Investment of A = Rs. 25000
Investment of B = Rs. 15000
Investment of C = Rs. 40000
 Therefore, the ratio of their investment is given by \[ = 25000{\text{ }}:{\text{ }}15000{\text{ }}:{\text{ }}40000 = 5{\text{ }}:{\text{ }}3{\text{ }}:{\text{ }}8\]
The sum of the ratios \[ = 5{\text{ }} + {\text{ }}3{\text{ }} + {\text{ }}8 = 16\]
 Therefore, Their shares of the profit will be $\dfrac{5}{{16}}$ th, $\dfrac{3}{{16}}$ th and $\dfrac{8}{{16}}\,\,{\text{th }}\left( {{\text{or }}\dfrac{1}{2}} \right)$ of the total profit respectively.
 Now, given that total profit in a year is Rs. 14400
 Share of A $ = 14400 \times \dfrac{5}{{16}} = Rs.4500\,$
 Share of B $ = 14400 \times \dfrac{3}{{16}} = Rs.2700\,$
 Share of C $ = 14400 \times \dfrac{1}{2} = Rs.7200\,$
Hence, the share of each out of a profit of Rs. 14,400 in a year is Rs. 4500, Rs. 2700, and Rs. 7200 respectively.


Note: Given that, three persons start a business and spend Rs. 25,000, Rs. 15,000 and Rs. 40,000 respectively. Therefore, find the ratio of their investment. Now note that, their share in the profit will be in the same ratio with that of their investment.
Alternate solution is given by,
It is given that three persons spend Rs. 25,000, Rs. 15,000 and Rs. 40,000 respectively.
Investment of A = Rs. 25000
Investment of B = Rs. 15000
Investment of C = Rs. 40000
 Then the total investment is given by taking their sum.
25000+15000+40000 = Rs.80000
Now, given that total profit in a year is Rs. 14400
 Then profit percentage is $\dfrac{{14400}}{{80000}} \times 100\% = 18\% $
Therefore, each person will get $18\% $ of their investment.
Share of A $ = 25000 \times \dfrac{{18}}{{100}}$ Rs.4500
Share of B $ = 15000 \times \dfrac{{18}}{{100}}$ Rs.2700
Share of C $ = 40000 \times \dfrac{{18}}{{100}}$ Rs.7200
Hence, the share of each out of a profit of Rs. 14,400 in a year are Rs. 4500, Rs. 2700, and Rs. 7200 respectively.