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)

Created: 1 year ago | Updated: 1 year ago

Updated: 1 year ago

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= $x + 16 % o f x = x + \frac{16 x}{100} = \frac{116 x}{100} T K .$

Again, price at 12% loss

$= (840 - x) - 12 % o f (840 - x) T k = (840 - x) - \frac{12 (840 - x)}{100} T K . = (840 - x) - \frac{2520 - 3 x}{25} T K . = \frac{2100 - 25 x - 2520 + 3 x}{25} T K . = \frac{18480 - 22 x}{25} T K .$

According to the question,

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