Evaluate the truth of each statement based on the properties of perfect squares and perfect cubes and prime factorization.
Consider the following statements: 1. 132651 is a perfect cube. 2. A number having 2, 3, 7 or 8 at unit's place is never a perfect square. 3. By multiplying 5808 by 7, it becomes a perfect square. Which of the above statement/statements is/are true?
Asked in GPSC Prelims CSP 1 2019 · Topic: Tertiary Sector (Definition and Characteristics of the Tertiary Sector)
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- A shopkeeper buys 12 toys and labels each with the same selling price. He sells 8 toys initially at 20% discount on the labelled price. Then he sells the remaining 4 toys at an additional 25% discount on the discounted price. Thus, he gets a total of Rs. 2112, and makes a 10% profit. With no discounts, his percentage of profit would have been how much?
- So, CP = 160. - Now, let's find the labelled price L using the sales information. - 8 toys were sold at a 20% discount on L. SP for these 8 toys = 8 (L (1 - 0.20)) = 8 (0.8L) = 6.4L. - The remaining 4 toys were sold at an additional 25% discount on the discounted price. The first discounted price was 0.8L. The second discount is 25% on 0.8L. SP for 4 (0.6L) = 2.4L. - The total selling price is the sum of the SPs of the two groups of toys. - Total SP = 6.4L + 2.4L = 8.8L. - We know the total SP is 2112. - 8.8L = 2112 - L = 2112 / 8.8 = 21120 / 88 = 240. - The labelled price of one toy is Rs. 240. - The cost price of one toy is Rs. 160. - The question asks for the profit percentage if no discounts were given. - If no discounts were given, the selling price of each toy would be the labelled price L = 240. - Profit per toy = SP - CP = 240 - 160 = 80. - Profit percentage = (Profit / CP) 100 = (80 / 160) 100 = (1/2) 100 = 50%. 37. Instead of dividing Rs. 117 among X, Y and Z in the ratio 1/2 : 1/3 : 1/4, by mistake it was divided in the ratio of 2 : 3 : 4. Who gains the most benefit and by how much?
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