Question

M started a business with Rs. 25,000. N joined him after 4 months with Rs 20,000. After 2 more months, M withdrew Rs. 10,000 of his capital and 2 more months later, N brought in Rs. 10,000 more. What should be the ratio in which they should share their profits at the end of the year?

Answer 1

Calculate who invested for how many months of the year and what amount was invested in each month in the business calculate the same thing for both of them and then find the ratio.

Complete step-by-step answer:
Suppose that M invested v in the month of january
So he was leading the business alone for 4 months and then in the month of april N joined the business by investing 20000
Agan after 2 months in the month of june M withdraws a total amount of 10000
And 2 months more later say in the month of august N invested 10000 more
So from january to june total investment for M was 25000
And from june to december the investment was 15000
Again from april to august the investment from N was 20000
And from september to december the investment from N alone was 30000
So from here it is clear that M did the business for 4 months
And N did the same business for 8 months
For M the investment was $(25000 \times 6) + (15000 \times 6)$
And for N the investment was $(20000 \times 4) + (30000 \times 4)$
So the profit share in the form of

\Rightarrow M:N = \left[ {(25000 \times 6) + (15000 \times 6)} \right]:\left[ {(20000 \times 4) + (30000 \times 4)} \right]\\\ \Rightarrow M:N = \left[ {150000 + 90000} \right]:\left[ {80000 + 120000} \right]\\\ \Rightarrow M:N = 240000:200000\\\ \Rightarrow M:N = 24:20\\\ \Rightarrow M:N = 6:4\\\ \Rightarrow M:N = 3:2 \end{array}$$ **Note:** The statements of the questions were tricky itself so it's best to write iot in layman terms by taking months and as I have elaborated in the answer section, decoding the question was the only key step and then the calculations were pretty simple.