Question

A and b started a business with a total capital of rs 30000. at the end of the year , they shared the profit in the ratio of their investments. if their capitals were interchanged, then a would have received 175% more than what he actually received. find the capital of b

Answer 1

Let investment of A =x=x
Then, investment of B =(30000−x)=(30000−x)

Ratio in which A and B shared their profit
=x:(30000−x)=x:(30000−x)

If the total profit is yy, profit that A gets
=yx30000  ⋯(1)=yx30000  ⋯(1)

If their capitals were interchanged, the ratio would be
=(30000−x):x=(30000−x):x

In this case, profit that A gets
=y(30000−x)30000  ⋯(2)=y(30000−x)30000  ⋯(2)

If their capitals were interchanged, then A would have received 175%175% more than what he actually received. 
i.e., A new profit = A's old profit + 175%175% of A's old profit.
i.e., A new profit =275%=275% of A's old profit.

y(30000−x)30000=yx30000×275100(30000−x)=x×114120000−4x=11x15x=120000x=8000y(30000−x)30000=yx30000×275100(30000−x)=x×114120000−4x=11x15x=120000x=8000

Capital of B =(30000−x)=(30000−x)
=(30000−8000)=22000