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A started a business with a capital of Rs.10000. Four months later, B joined him and 2 more months later, C joined them in the partnership. If at the end of the year, all of them got an equal share of profit, what was C’s investment?
(a) Rs.15000
(b) Rs.20000
(c) Rs.18000
(d) Rs.22000

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Last updated date: 21st Jul 2024
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Answer
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Hint: In this type of question we have to use the concept of partnership. We know that the share of profit is getting divided in the same way as that of the investment in the business. So depending on the share of profit we can find the share of the investment for each one of them.

Complete step by step answer:
Here, we have given the investment of A, B and C through which they got some profit at the end of the year and all of them got an equal share of profit. We need to find the C’s investment.
Here we have given that A started a business with a capital of Rs.10, 000. So the investment of A is for the full one year and as 1 year has 12 months
\[\Rightarrow \text{Total Investment of A = Rs}\text{.10000}\times \text{12 = Rs}\text{.120000}\]
Now, we have given that at the end of the year A, B and C all of them got an equal share of profit that means their investments must be the same.
Now, as B joined A after 4 months, we can say that the total investment of B is for \[12-4=8\] months which must be the same as that of the total investment of A.
Also we have given that C joined them 2 more months later than B that means for \[12-6=6\] months. Here also the investment of C must be the same as that of the total investment of A.
\[\Rightarrow \text{Total Investment of C for 6 months = Total Investment of A for one year}\]
Let us suppose that the C’s investment is Rs. \[x\]
\[\begin{align}
  & \Rightarrow \text{6}x\text{ = Total Investment of A for one year} \\
 & \Rightarrow 6x=Rs.120000 \\
 & \Rightarrow x=\dfrac{Rs.120000}{6} \\
 & \therefore x=Rs.20000 \\
\end{align}\]
Hence, C’s investment = Rs.20000

So, the correct answer is “Option b”.

Note: In this type of question students should not forget about considering the C’s investment for 6 months only and not for 12 months. Here, students have to remember that the profit is divided as per the investment of the partners so as the profit is equally distributed the investment of each partner must be the same.