The cost of two watches taken together is Tk. 840. If by selling one at a profit of 16% and the other at a loss of 12%, there is no loss or gain in the whole transaction, find the cost of each of the two watches. (profit and loss)

বলা হচ্ছে যে, দুটি ঘড়ির একত্রে ক্রয়মূল্য 840 টাকা। একটি ঘড়ি 16% লাভে এবং অপরটি 12% ক্ষতিতে বিক্রয় করলে লাভ/ক্ষতি কোনটাই হয় না। প্রতিটি ঘড়ির ক্রয়মূল্য কত?

Let, the cost price of one watch is x Tk. 

The cost price of another watch is (840-x) Tk.

 Selling price at 16% profit=$x+16\% of x= x+\frac{16x}{100}=\frac{116x}{100}TK.$

Again, price at 12% loss

$$\begin{gathered} = (840-x)-12\% of (840-x) Tk \\ =\left(840-x\right)-\frac{12\left(840-x\right)}{100}TK. \\ =\left(840-x\right) - \frac{2520-3x}{25}TK. \\ = \frac{2100-25x-2520+3x}{25}TK. \\ = \frac{18480-22x}{25}TK. \end{gathered}$$

According to the question, 

$$\begin{gathered} \frac{116x}{100}+\frac{18480-22x}{25}=840 \\ \Rightarrow \frac{116x+73920-88x}{100}=840 \\ \Rightarrow 28x+73920=84,000 \\ \Rightarrow 28x=84,000-73,920 \\ \Rightarrow 28x=10,080 \\ \Rightarrow x=\frac{10080}{28} \\ \therefore x=360 \end{gathered}$$

The cost price of one watch is 360 Tk.

The cost price of another watch = (840-360)= 480 Tk. 

ans. The cost price of one watch is 360 Tk. & another watch is 480 Tk.