Question

A invested Rs. 5000 in a business. After 4 months B joined him by investing Rs. 4800. After a further 2 months, C joined them Rs. 5200. If after the end of year, they earned a total profit of Rs. 14,400, then what is the difference between the shares of A and B?

Answer 1

Hint: Investment period of A is 12 months, B is 8 months and C is 6 months. So, their profit will depend upon the ratio of their distribution and investment period. So, the profit ratio of A, B and C are in the ratio, $5000\times 12:4800\times 8:5200\times 6$ and the difference in the shares of the partners is given by, $\dfrac{\text{share ratio difference}}{25+16+13}\times 14400$.

Complete step-by-step answer:
It is given in the question that, A invested Rs. 5000 in a business. After 4 months B joined him by investing Rs. 4800. After a further 2 months, C joined them Rs. 5200. After the end of year, they earned a total profit of Rs. 14,400, then we were asked to find the difference between the shares of A and B.
As the share ratio will depend upon their invested amount and investment time. Here, A has invested Rs. 5000 for 12 months as he invested first, B has invested Rs. 4800 for 8 months as he joined 4 months after A and C has invested Rs. 5200 for 6 months as he joined 2 months after B.
So, the ratio of the shares of profit of A: B: C is given by, amount shared $\times $ time. So, we get,
$\begin{align}
  & 5000\times 12:4800\times 8:5200\times 6 \\
 & 50\times 12:48\times 8:52\times 6 \\
 & 600:384:312 \\
 & 25:16:13 \\
\end{align}$
So, the ratio of profit shared by A: B: C is 25: 16 :13.
We know that the total annual profit is Rs. 14,400.
So, the difference in shares of A and B is given by,
$\dfrac{\text{difference in ratio of their profit}}{\text{sum of ratios}}\times 14400$
Here, we have to find the difference in shares of A and B. We know that A has shares 25 and B has shares 16, so we get,
$\begin{align}
  & =\dfrac{25-16}{25+16+13}\times 14400 \\
 & =\dfrac{9}{54}\times 14400 \\
 & =\dfrac{14,400}{6} \\
 & =Rs.2400 \\
\end{align}$
Thus, the difference in shares of A and B profit is Rs. 2400.

Note: Many students make mistakes in the last step, they may take the sum of ratios as 100, assuming that the total of anything in percentage is 100, but this is not true here. We have to take the sum of the ratios as 25+16+13, which is 54 and not 100. Thus, it is recommended to do the calculations carefully.