Question
A chord, at a distance of 1 unit from the centre, has a
length equal to k² sin (π/4) and the radius of the circle is (-k) sin(π/3). What is the value of k, if k is an integer?Solution
Radius = (-k) sin(π/3) = -√3k/2 Distance from chord to centre = OM = 1unit MR = length of chord/2 = [k2sin(π/3)]/2 = k2/2√2 In triangle OMR, => OM2 + MR2 = OR2 ⇒ 1 + k4/8 = 3k2/4 ⇒ k4 - 6k2 + 8 = 0 By hit and trial method, we get k = -2
An item's price is set 25% higher than its cost price. After applying two consecutive discounts of 20% and 25%, it is sold for Rs. 1,500. Calculate the ...
An article Marked price is 30% above its cost price and it is sold at a discount of 10% making a profit of Rs.850.Then, what will be the selling price o...
A invested Rs. X in a business. After four months B Joined him with Rs. 7X and A double his investment. If at the end of the years total profit is Rs. 4...
The cost price of 15 mangoes is Rs.220. Because of bad quality of mangoes, the shopkeeper has to sell mangoes at a loss that is equal to selling price o...
Viru has Rs. 9000. He gives this money to Mahi on simple interest and after 4 years received the double amount. If the interest rate is 5% more than the...
- The ratio of the marked price and cost price of an item is 9:6. If the discount allowed is equal to the profit earned, find the profit percentage.
A shopkeeper bought a mobile phone for Rs. 18,500 and sold it for Rs. 21,275. What percentage of profit did he earn in this transaction?
A trader marked an article 20% above its cost price and sold it after allowing a discount of 15%. If the transaction resulted in a profit of Rs. 22, the...
Ram sold a copy at a profit of 15%. Had he sold it for Rs 48 more, 21% would have been gained. Find the cost price?
Ravi bought two products, ‘M’ and ‘N’, at the same price. He added a markup of 20% on ‘M’ and 50% on ‘N’. Then, he gave a discount of Rs...
Relevant for Exams:
