Question

A and B started a business in partnership investing Rs.20000 and Rs.15000 respectively. After six months, C joined them with Rs.20000. What will be B's share in the total profit of Rs.25000 earned at the end of 2 years from the starting of the business?
\[\begin{align}
  & A.Rs.7500 \\
 & B.Rs.9000 \\
 & C.Rs.9500 \\
 & D.Rs.10000 \\
\end{align}\]

Answer 1

Hint: In this question, we are given the investment of A, B, and C for a business through which they got a profit of Rs.25000. We need to tell the B's share out of the profit after 2 years. For this, we will first find the ratio of their investment for 2 years. A's and B's investment will be for 24 months (2 years) and C's investment will be for 18 months (6 months late than A and B). Adding calculation share, we will use the following formula to calculate the share of B.
 $ \text{B }\!\!'\!\!\text{ s share}=\dfrac{\text{B }\!\!'\!\!\text{ s ratio number}}{\text{Total ratio}}\times \text{Total profit} $ .

Complete step by step answer:
Here we are given the investment of A as Rs 20000, investment of B as Rs.15000, and investment of C as Rs.20000.
Now since A and B started the business so they invested for the full 2 years. 1 year has 12 months. So 2 year = 24 months. Therefore, A and B invested for 24 months.
Investment of A becomes $ \Rightarrow Rs.20000\times 24=Rs.480000 $ .
Similarly investment of B becomes $ \Rightarrow Rs.15000\times 24=Rs.360000 $ .
Now C joined them later after 6 months so his investment will be for (24-6) months i.e. 18 months
So investment of C becomes $ \Rightarrow Rs.20000\times 18=Rs.360000 $ .
Now let us calculate the ratio of their shares in investment for the company, we have the ratio as
 $ A:B:C=480000:360000:360000 $ .
Dividing all the ratios by common ratio 120000 we get, A:B:C = 4:3:3.
Therefore A's share in the business is 4x, B's share is 3x and C's share is 3x if x is the common ratio. Therefore, their profit will also get divided in the same way. Now total profit is Rs.25000 which is to be divided among A, B, C in the ratio 4:3:3.
Total ratio is equal to 4+3+3 = 10.
So, A's share $ \Rightarrow \dfrac{4}{10}\times \text{Total profit} $ .
B's share $ \Rightarrow \dfrac{3}{10}\times \text{Total profit} $ .
C's share $ \Rightarrow \dfrac{3}{10}\times \text{Total profit} $ .
We require B's share only. So the share of B can be calculated as, $ \Rightarrow \dfrac{3}{10}\times \text{Rs}\text{.25000}\Rightarrow \text{3}\times \text{2500=Rs}\text{.7500} $ .
Hence B's share in the total profit will be Rs.7500.
Hence option A is the correct answer.

Note:
Students should not forget about considering the C's investment for 18 months only and not 24 months. Students can make mistake while calculating ratios. Make sure to divide that ratio by the same (common) ratio only. For dividing an amount of Rs.P between A and B if their ratio is x:y we use the formula as,
 $ \text{A }\!\!'\!\!\text{ s share}=\dfrac{x}{x+y}\times P\text{ and B }\!\!'\!\!\text{ s share}=\dfrac{y}{x+y}\times P $ .