Question

One says, “Give me a hundred, friend! I shall then become twice as rich as you”.

The other replies, “If you give me ten, I shall be six times as rich as you”.

Tell me what is the amount of their (respective) capital?

Answer 1

Step 1: Form a pairs of equation based on the given statement of the problem

Let us assume that

One friend has capital amount$\text{= x}$

Other friend has capital amount$\text{= y}$

According to the question,
$\begin{array}{rcl}& & \text{x+100 = 2}\left(\text{y-100}\right)\\ & & \text{x+100 = 2y-200}\\ & & \text{x-2y = -300 ----------------(i)}\end{array}$
also,
$$\begin{gathered} 6\left(\text{x-10}\right)=\text{y+10} \\ \text{6x-60 = y+10} \\ \text{6x-y = 70 -------------------(ii)} \end{gathered}$$

Step 2: Solve above pairs of equations
Multiply equation (ii) by $2$, and then subtract equation (i) from equation (ii) we get
$\begin{array}{rcl}12x-2y-\left(x-2y\right)& =& 140-\left(-300\right)\\ 12x-2y-x+2y& =& 140+300\\ 11x& =& 440\\ x& =& \frac{440}{11}\\ x& =& 40\end{array}$
Substitute $x=40$in equation (i),
$\begin{array}{rcl}x-2y& =& -300\\ 40-2y& =& -300\\ -2y& =& -300-40\\ 2y& =& 340\\ y& =& \frac{340}{2}\\ y& =& 170\end{array}$

Hence, the amount of first friend capital is$\text{Rs. 40}$ and of second friend capital is$\text{Rs. 170}$.