In a business A invests Tk. 600 more than B. The capital of B remained invested for 7 12 months, while the capital of A remained invested for 2 more months. If the total profit be Tk. 620 and B gets Tk. 140 less than what A gets, then what will be the amount of A's capital? (Partnership (অংশীদারী কারবার))

প্রশ্নে বলা হচ্ছে একটি ব্যবসায় A, B অপেক্ষা 600 টাকা বেশি বিনিয়োগ করে। ঐ ব্যবসায় B এর টাকা খেটেছে $7 \frac{1}{2}$ মাস এবং A এর টাকা খেটেছে B এর চেয়েও 2 মাস বেশি। ঐ ব্যবসায় মোট মুনাফা হয়েছিল 640 টাকা এবং মুনাফা হিসেবে B, A অপেক্ষা 140 টাকা কম পেল । A এর মূলধন কত ছিল?

Let, A's investment is Tk. x & B's investment is Tk. (x - 600)

Given, B's capital works for 7.5 months

∴ A's capital works for = 7.5 + 2 = 9.5 months

Assume again that the duration of the business was for n months.

Now, if B gets Tk. y as profit

∴ A will get Tk. (y+140) as profit.

According to question

$$\begin{gathered} y+140+y=620 \\ \Rightarrow 2y=620-140=480 \\ \therefore y = \frac{480}{2} = 240 \end{gathered}$$

∴  B gets as profit Tk. 240 & A gets as profit Tk. (140+240) = Tk. 380.

Now, we can write

$$\begin{gathered} \frac{9.5x}{n} \times \frac{7.5 \left(x-600\right)}{n} = 380 : 240 \\ \Rightarrow \frac{9.5x}{n} \times \frac{n}{7.5 \left(x-600\right)} = \frac{380}{240} = \frac{19}{12} \\ \Rightarrow \frac{9.5x}{7.5x - 4500} = \frac{19}{12} \\ \Rightarrow 114x = 142.5x = 85,500 \\ \Rightarrow 142.5x -114x = 85,500 \\ \Rightarrow 28.5x = 85,500 \\ \therefore x = \frac{85500}{28.5} = 3000 \\ \mathit{a}\mathit{n}\mathit{s}\mathbf{:} A\text{'}s capital was Tk. 3,000. \end{gathered}$$