Question

A and B start a business with investment of Rs 5000 and Rs 4500 respectively. After 4 months, A takes out half of his capital. After two more months, B takes out one – third of his capital while C joins them with a capital of Rs 7000. At the end of year they earn a profit of Rs 5080. Find the share of each member in the profit.
(a) A – Rs 1400, B – Rs 1900, C – Rs 1780
(b)A – Rs 1600, B – Rs 1800, C – Rs 1680
(c) A – Rs 1800, B – Rs 1500, C – Rs 1780
(d) None of these

Answer 1

Hint: First of all find the share of A, B and C at the end of one year. The share at the end of 1 year is calculated by multiplying 5000 by 4 then after 4 months he withdrew 2500 from the capital so for remaining 8 months, its share will be found by multiplying 2500 by 8 and then add the result of multiplication of 5000 by 4 with multiplication of 2500 by 8. Similarly, calculate for B. The share for C is calculated by multiplying 7000 by 6 because C has joined the investment after 6 months. To calculate the share of profit for each person we are going to divide the share of money at the end of the year for each person by total share and then multiply this result by 5080.

Complete step-by-step answer:
We are going to find the individual share of A, B and C at the end of one year.
First of all we are going to find the share of A:
A invested 5000 then took it out after 4 months so the money accumulated after 4 months is the multiplication of 5000 by 4 then he withdrew 2500 after 4 months so the money remaining is 2500 so the amount accumulated from this month to the end of the year is equal to the multiplication of 2500 by 8. Hence, the amount of share at the end of one year for A is:
 $ \begin{align}
  & 5000\times 4+2500\times 8 \\
 & =20000+20000 \\
 & =40000 \\
\end{align} $
Now, we are going to find the share of B at the end of 1 year. B invested 4500 in the beginning then after 6 months he withdrew 1500 so he is remaining with 3000 so the money accumulated over 6 months is $ 4500\times 6 $ and for the remaining 6 months the amount accumulated is $ 3000\times 6 $ . Hence, the share of B at the end of 1 year is:
 $ \begin{align}
  & 4500\times 6+3000\times 6 \\
 & =27000+18000 \\
 & =45000 \\
\end{align} $
The share of C at the end of 1 year is calculated by multiplying 7000 by 6.
 $ \begin{align}
  & 7000\times 6 \\
 & =42000 \\
\end{align} $
It is given that the total profit at the end of 1 year is 5080.
The profit share of each individual is calculated by dividing that individual share to the total share of A, B and C then multiplying this result with total profit given.
Total share is equal to:
  $ \begin{align}
  & 40000+45000+42000 \\
 & =127000 \\
\end{align} $
The annual profit share for A is:
 $ \begin{align}
  & \dfrac{40000}{127000}\times 5080 \\
 & =1600 \\
\end{align} $
The annual profit share for B is:
 $ \begin{align}
  & \dfrac{45000}{127000}\times 5080 \\
 & =1800 \\
\end{align} $
The annual profit share for C is:
 $ \begin{align}
  & \dfrac{42000}{127000}\times 5080 \\
 & =1680 \\
\end{align} $
From the above, the correct option is (b).

Note: One of the plausible mistakes that could happen is the calculation mistake. And the mistake that could happen is in the investment of B, B withdrew one third of its capital invested. The capital of B is Rs 4500 so one third of 4500 is 1500 so you might mistakenly multiply 1500 by 6 for the share of B calculations but we have to multiply the difference of 1500 and 4500 by 6.