Subject
Quantitative Aptitude
Topic
Profit & Loss
A trader paid Tk 300 for a shipment of x identical pens. The trader gave two pens free of cost and sold each for Tk. 5 more than the average cost of the x pens. If the total revenue from the sale of the pens was Tk. 120 more than the cost of the shipment, how many pens were in the shipment?
A trader paid Tk 300 for a shipment of x identical pens. The trader gave two pens free of cost and sold each for Tk. 5 more than the average cost of the x pens. If the total revenue from the sale of the pens was Tk. 120 more than the cost of the shipment, how many pens were in the shipment?
ক)
20খ)
24গ)
25ঘ)
30ঙ)
NoneExplanation
ধরি, জাহাজে থাকা কলমের সংখ্যা = x টি। প্রতিটি কলমের গড় খরচ = 300 / x টাকা। বিনামূল্যে দেওয়া কলমের সংখ্যা = 2 টি। বিক্রি করা কলমের সংখ্যা = x - 2 টি। প্রতিটি কলমের বিক্রয়মূল্য = (300 / x) + 5 টাকা। মোট বিক্রয় আয় = (x - 2) * [(300 / x) + 5] টাকা। জাহাজের খরচের চেয়ে মোট বিক্রয় আয় 120 টাকা বেশি। সুতরাং, (x - 2) * [(300 / x) + 5] = 300 + 120। ⇒ (x - 2) * (300 + 5x) / x = 420। ⇒ (x - 2) * (300 + 5x) = 420x। ⇒ 300x + 5x² - 600 - 10x = 420x। ⇒ 5x² - 130x - 600 = 0। ⇒ x² - 26x - 120 = 0। ⇒ x² - 30x + 4x - 120 = 0। ⇒ x(x - 30) + 4(x - 30) = 0। ⇒ (x - 30)(x + 4) = 0। সুতরাং, x = 30 বা x = -4। যেহেতু কলমের সংখ্যা ঋণাত্মক হতে পারে না, তাই x = 30। সুতরাং, জাহাজে থাকা কলমের সংখ্যা হলো 30 টি।Related questions
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