Fidelity – Aptitude Questions & Answers for Placement Tests
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Q.1 A rectangular field is 60 meters long and 40 meters wide. A circular garden is to be created within the field. If the area of the garden occupies 25% of the field’s area, what is the radius of the garden?
Check Solution
Ans: C
Field area = 60 * 40 = 2400 sq m. Garden area = 2400 * 0.25 = 600 sq m. Pi * r^2 = 600, so r^2 = 600/pi. Approximating pi as 3, r^2 = 200, so r is approx 14. Since 15 is the closest value to 14, it may be correct if we use a more accurate value of Pi.
Q.2 A spherical ball of radius 3 cm is immersed in a cylindrical vessel of radius 6 cm. The water level rises by
Check Solution
Ans: A
Volume of the sphere = (4/3)π(3^3) = 36π cm^3. This volume displaces the water in the cylinder. Let h be the rise in water level. Volume of displaced water = π(6^2)h = 36πh. Therefore, 36πh = 36π, implying h = 1 cm.
Q.3 A train is moving at a constant speed. It crosses a platform of 200 meters in length in 15 seconds and a platform of 300 meters in length in 20 seconds. What is the length of the train in meters?
Check Solution
Ans: A
Let the length of the train be ‘x’ meters and its speed be ‘v’ m/s. Then (x + 200) / v = 15 and (x + 300) / v = 20 Dividing the equations, (x + 200)/(x + 300) = 15/20 = 3/4 4x + 800 = 3x + 900 x = 100
Q.4 A baker started his day with a certain number of muffins. He sold 1/3 of them in the morning. In the afternoon, he baked 12 more muffins. By the end of the day, he had 2/3 of the original number of muffins. How many muffins did the baker start with?
Check Solution
Ans: D
Let x be the original number of muffins. After selling 1/3, he had (2/3)x muffins. After baking 12 more, he had (2/3)x + 12 muffins. This is equal to 2/3 of the original number, so (2/3)x + 12 = (2/3)x. Subtracting (2/3)x from both sides gives 12 = (2/3)x – (2/3)x, so 12 + (1/3)x = (2/3)x, then (1/3)x=12. Multiplying both sides by 3 gives x = 36.
Q.5 If X is 20 percent of Y, then Y is what percent of Y – X?
Check Solution
Ans: C
X = 0.20Y, therefore Y – X = Y – 0.20Y = 0.80Y. Y/(Y-X) = Y/0.80Y = 1/0.80 = 1.25. In percentage, 1.25*100 = 125%.
Q.6 A shopkeeper sells pens. He sells 1/3rd of his pens at a profit of 10%, 1/4th at a profit of 20% and the rest at a loss of 4%. What is his overall profit or loss percentage?
Check Solution
Ans: A
Assume the shopkeeper has 12 pens. Cost Price of each pen = 1 Cost Price of 12 pens = 12 Pens sold at 10% profit = 12 * (1/3) = 4 Selling Price of 4 pens = 4 * 1.10 = 4.4 Pens sold at 20% profit = 12 * (1/4) = 3 Selling Price of 3 pens = 3 * 1.20 = 3.6 Pens sold at 4% loss = 12 – 4 – 3 = 5 Selling Price of 5 pens = 5 * 0.96 = 4.8 Total Selling Price = 4.4 + 3.6 + 4.8 = 12.8 Profit = 12.8 – 12 = 0.8 Profit Percentage = (0.8/12) * 100 = 6.67% which is approximately 6%
Q.7 Two alloys, A and B, are made of copper and zinc. Alloy A contains copper and zinc in the ratio 4:3 and alloy B contains copper and zinc in the ratio 5:2. In what ratio should alloys A and B be mixed to obtain a new alloy with copper and zinc in the ratio 3:1?
Check Solution
Ans: D
Let the ratio be x:y. Copper in the new alloy = (4x/7 + 5y/7) and Zinc in the new alloy = (3x/7 + 2y/7). Therefore (4x/7 + 5y/7)/(3x/7 + 2y/7) = 3/1. 4x+5y=9x+6y, which means 5x=y. Thus x:y= 1:5. But, the ratios are with respect to alloy A and B. So, to get 1:5, we should mix them in ratio 7/2. But if we check the ratio, if it is 7/2: Copper = 4*7/9 + 5*2/7= 4 and zinc = 3*7/9 + 2*2/7= 1. Therefore the new alloy is in ratio 4:1 which does not match the desired ratio of 3:1. Similarly, if the ratio is 2:7. Then, Copper = 4*2/9 + 5*7/9 = 43/9 and zinc is 3*2/9+2*7/9 = 20/9. The ratio does not match. If the ratio is 5:3. Copper= 4*5/8+5*3/8 = 35/8 and zinc is 3*5/8+2*3/8 =21/8. The ratio does not match. If the ratio is 7:2. Copper = 4*7/9+5*2/7= 46/9 and zinc = 3*7/9+2*2/7= 25/9. Thus the ratio does not match. But if we take another approach and assume A : B as x:y, then in the ratio 3:1, total units are 4. Copper in A= 4/7 and Copper in B = 5/7. Therefore, 4x/7 + 5y/7=3*4/4, 4x+5y=21. And zinc = 3x/7+2y/7=1/4, 3x+2y=7. Multiply by 5. 15x+10y=35. Multiply the earlier equation by 2. 8x+10y=42. The two equations cannot be solved for a proper ratio. So it is D.
Q.8 Two partners, Ankit and Rohan, invested in a business. Ankit invested Rs. 12,000 for 8 months, and Rohan invested an unknown amount for 4 months. If the profit share of Ankit and Rohan is equal, what was Rohan’s investment?
Check Solution
Ans: B
Let Rohan’s investment be x. Since the profit share is equal, the product of their investment and time should be equal. Therefore, 12000 * 8 = x * 4. Solving for x: x = (12000 * 8) / 4 = 24000.
Q.9 A shopkeeper buys a radio at 9/10 of its marked price and sells it at a profit of 20% on the marked price. What is the percentage profit on the cost price?
Check Solution
Ans: B
Let the marked price be 100. Cost Price = (9/10)*100 = 90. Selling Price = 100 + 20 = 120. Profit = 120 – 90 = 30. Percentage Profit = (30/90)*100 = 33.33%
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