Question

A and B started a business with a total capital of Rs. 30,000. 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

Hint: We will first start by letting the capital invested by A as x. So, we have the capital by B as Rs. 30,000 – x. Then we will assume the profit to be y and find their respective profit in the first and second cases. Then we will use the fact that A has received 175% more than he actually received by A.

Complete step-by-step solution -
Now, we have been given that A and B started a business with total capital Rs. 30,000.
Now, we let the capital invested by A = Rs. x
So, we have the capital invested by B = Rs. 30,000 – x
Now, we know that the profit is in the ratio of their investment. So, we let profit = Rs. y
Now, we have the profit of A and B in $A:B=x:30,000-x$. So, we have the profit of A = xy and profit of B = y (30,000 – x).
Now, in the second case we have been given that the capital of A and B are interchanged. So, we have capital invested by A = Rs. 30,000 – x
Capital invested by B = x.
So, we have the profit of A and B in the second case as $30,000-x:x$. So, we have the profit of A = y(30,000 – x) and the profit of B = y (x).
Now, we have been given in question that,
New profit of A = old profit of A + 175% of old profit of A
$y\left( 30,000-x \right)=xy+\dfrac{175}{100}xy$
Now, we cancel y on both sides. So, we have,
$\begin{align}
 \Rightarrow & 30,000-x=x+\dfrac{35}{20}x \\
 \Rightarrow & 30,000-x=x+\dfrac{7}{4}x \\
 \Rightarrow & 30,000=2x+\dfrac{7}{4}x \\
 \Rightarrow & 30,000=\dfrac{8x+7x}{4} \\
 \Rightarrow & 30,000=\dfrac{15x}{4} \\
 \Rightarrow & \dfrac{30,000\times 4}{15}=x \\
 \Rightarrow & 2000\times 4=x \\
 \Rightarrow & 8000=x \\
\end{align}$
So, we have capital invested by B,
$\begin{align}
  & =30,000-x \\
& =30,000-8,000 \\
 & =22,000 \\
\end{align}$
Hence, the capital invested by B is Rs. 22,000.

Note: It is important to note that the profit of A and B are in the ratio $x:30,000-x$ for the first case and therefore we have the profit of A = XY and B = y(30,000 – x) because the profit of both A and B is y. Also, it is important to note that for the second case also the total profit remained the same but the distribution got changed.