TCS Aptitude Questions & Answers for Placement Tests
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Q.1 If g(x) = |x|, what is the shape of g(x)?
Check Solution
Ans: B
The absolute value function creates a V-shape.
Q.2 A train starts from Mumbai at 6:00 AM and reaches Pune at 9:00 AM. Another train starts from Pune at 7:00 AM and reaches Mumbai at 10:00 AM. At what time do the two trains cross each other?
Check Solution
Ans: C
Let the distance between Mumbai and Pune be D. Train 1’s speed is D/3 (distance/time) Train 2 starts 1 hour later, so at 7:00 AM, Train 1 has traveled D/9 distance. Remaining distance = D – D/9 = 8D/9. Relative speed = D/3 + D/3 = 2D/3 Time to meet = (8D/9) / (2D/3) = 4/3 hours = 1 hour 20 minutes. Train 2 starts at 7:00 AM. Therefore, they meet at 7:00 AM + 1 hour 20 minutes = 8:20 AM
Q.3 Two friends, Anika and Rohan, took a quiz. Anika scored 70% and missed the passing score by 10 marks. Rohan scored 80% and passed the quiz by 20 marks. What was the maximum possible marks for the quiz?
Check Solution
Ans: B
Let ‘x’ be the maximum marks. Anika’s score = 0.7x and she missed by 10. Rohan’s score = 0.8x and he passed by 20. Passing score is the same for both: 0.7x + 10 = 0.8x – 20. Therefore, 0.1x = 30, and x = 300.
Q.4 A rare species of bacteria doubles its population every 12 hours. A biologist observes a colony that reaches a size of 8000 bacteria after 6 days. How many bacteria were present 24 hours prior to reaching 8000?
Check Solution
Ans: B
6 days is 144 hours. 24 hours before reaching 8000 means 120 hours. Since the bacteria doubles every 12 hours, in 24 hours (2 doublings), the colony size reduces to 1/4. Therefore, 8000 / 4 = 2000 bacteria.
Q.5 Two friends, Rohan and Sohan, are participating in a race. Rohan runs at a constant speed of 12 meters per second. Sohan runs at a constant speed, but his speed is slower than Rohan’s. The distance between the starting and finishing point is 180 meters. If Sohan finishes the race 5 seconds after Rohan, what is Sohan’s speed in meters per second?
Check Solution
Ans: C
Rohan’s time = 180/12 = 15 seconds. Sohan’s time = 15 + 5 = 20 seconds. Sohan’s speed = 180/20 = 9 meters/second.
Q.6 A shopkeeper has 120 articles. Initially, 30% of the articles were defective. He sold a certain number of non-defective articles and discovered that the percentage of defective articles among the remaining articles was now 40%. Then he sold all the remaining articles. How many non-defective articles did he sell initially?
Check Solution
Ans: C
Initially, defective articles = 120 * 30% = 36. Non-defective articles = 120 – 36 = 84. Let ‘x’ be the number of non-defective articles sold. Remaining articles = 120 – x. Defective articles percentage = 40%. Defective articles remaining are still 36. Therefore, 36 / (120 – x) = 40/100, which simplifies to 36 * 100 = 40 * (120 – x). 3600 = 4800 – 40x. 40x = 1200. x = 30.
Q.7 A vessel contains 60 liters of milk. 10 liters of milk are taken out and replaced with water. This process is repeated two more times. What is the quantity of milk left in the vessel?
Check Solution
Ans: C
After the first replacement, milk left = 60 * (50/60) = 50 liters. After the second replacement, milk left = 50 * (50/60) = 41.67 liters. After the third replacement, milk left = 41.67 * (50/60) = 34.72 liters. Therefore the exact calculation: 60*(5/6)*(5/6)*(5/6) = 34.72. But since there is no direct solution available, we may approximate to find the closest answer. 60 * (5/6) * (5/6) * (5/6) = 34.72 litres. However, the closest solution is 35 litres.
Q.8 A leaky tap drips water at a constant rate. In the first minute, it drips 10 ml of water. In each subsequent minute, the amount of water dripped decreases by 20% of the amount dripped in the previous minute. A bucket with a capacity of 100 ml is placed under the tap. Approximately, in how many minutes will the bucket be full?
Check Solution
Ans: A
Minute 1: 10 ml. Minute 2: 10 * 0.8 = 8 ml. Minute 3: 8 * 0.8 = 6.4 ml. Minute 4: 6.4 * 0.8 = 5.12 ml. Minute 5: 5.12 * 0.8 = 4.096 ml. Minute 6: 4.096 * 0.8 = 3.2768 ml. Total after 4 minutes: 10 + 8 + 6.4 + 5.12 = 29.52 ml Total after 5 minutes: 29.52 + 4.096 = 33.616 ml Total after 6 minutes: 33.616 + 3.2768 = 36.8928 ml. The sum will converge to 50 ml if continuing indefinitely. It needs far more water than that. It is obviously not B or C or D.
Q.9 A rocket is launched vertically upwards with an initial velocity of 100 m/s. Assuming constant deceleration due to gravity (g = 9.8 m/s²), what is the maximum height reached by the rocket?
Check Solution
Ans: A
v² = u² + 2as, where v = 0 m/s (final velocity at max height), u = 100 m/s (initial velocity), a = -9.8 m/s² (acceleration due to gravity), and s = maximum height. 0 = 100² + 2(-9.8)s. s = 10000 / 19.6 = 510.2 m
Q.10 Antonym of ‘Ephemeral’
Check Solution
Ans: A
Ephemeral means lasting for a very short time. The antonym is something that lasts.
Q.11 A train leaves Mumbai for Delhi at 6 AM, traveling at a speed of 60 kmph. Another train leaves Delhi for Mumbai at 9 AM, traveling at a speed of 75 kmph. The distance between Mumbai and Delhi is 840 km. At what approximate time will the two trains meet?
Check Solution
Ans: A
The first train travels for 3 hours (from 6 AM to 9 AM) before the second train starts. In these 3 hours, it covers 60 kmph * 3 hours = 180 km. The remaining distance between the two trains at 9 AM is 840 km – 180 km = 660 km. The relative speed of the two trains is 60 kmph + 75 kmph = 135 kmph. The time taken for the two trains to meet after 9 AM is 660 km / 135 kmph = 4.89 hours, which is approximately 4 hours and 53 minutes. Therefore, the trains will meet around 9 AM + 4 hours and 53 minutes = 1:53 PM. Closest option available is 2 PM
Q.12 A bag contains 7 red balls and 5 blue balls. Two balls are drawn at random. What is the probability that one ball is red and the other is blue?
Check Solution
Ans: A
Total number of balls = 7 + 5 = 12. The number of ways to select 2 balls from 12 is 12C2 = (12*11)/2 = 66. The number of ways to select 1 red ball from 7 is 7C1 = 7, and the number of ways to select 1 blue ball from 5 is 5C1 = 5. Therefore, the number of ways to select 1 red and 1 blue ball is 7 * 5 = 35. The probability is 35/66.
Q.13 The expression 2(x^2) + nx – 12 leaves a remainder of 6 when divided by x + 2. What is the value of n?
Check Solution
Ans: B
Using the Remainder Theorem, substitute x = -2 into the expression and set it equal to 6: 2(-2)^2 + n(-2) – 12 = 6. Simplifying, we get 8 – 2n – 12 = 6, which simplifies to -2n – 4 = 6. Adding 4 to both sides gives -2n = 10. Dividing both sides by -2 gives n = -5.
Q.14 A rectangular container has a base of 60 cm by 40 cm. If 48 liters of liquid are poured into the container, what will be the height of the liquid?
Check Solution
Ans: B
Volume of liquid = 48 liters = 48000 cm^3. Area of base = 60 cm * 40 cm = 2400 cm^2. Height = Volume / Area = 48000 cm^3 / 2400 cm^2 = 20 cm.
Q.15 A train travels 300 km at a uniform speed. If the speed had been 10 km/hr more, it would have taken 1 hour less for the same journey. Find the original speed of the train in km/hr.
Check Solution
Ans: B
Let the original speed be x km/hr. Then, 300/x – 300/(x+10) = 1. Simplifying, x^2 + 10x – 3000 = 0. Solving for x, we get x = 50 or x = -60. Since speed cannot be negative, x = 50 km/hr.
Q.16 A vessel contains 80 liters of milk. From this vessel, 8 liters of milk is taken out and replaced by water. This process is repeated twice more. How much milk is now contained in the vessel?
Check Solution
Ans: A
The formula for this type of problem is: Final quantity = Initial quantity * (1 – (Quantity removed / Total quantity))^Number of times process is repeated. In this case: Final Milk = 80 * (1 – (8/80))^3
Q.17 A pipe can fill a tank in 20 hours, but due to a leak in the bottom, it takes 24 hours to fill the tank. If the tank is full, how much time will the leak take to empty the full tank?
Check Solution
Ans: C
Let the capacity of the tank be LCM(20, 24) = 120 units. Pipe’s filling rate is 120/20 = 6 units/hour. Pipe with leak’s filling rate is 120/24 = 5 units/hour. Leak’s emptying rate = 6 – 5 = 1 unit/hour. Time taken by the leak to empty the full tank = 120/1 = 120 hours.
Q.18 X and Y can complete a task in 12 days. Y and Z can complete the same task in 15 days, and X and Z can complete it in 20 days. How many days will it take X to complete the task alone?
Check Solution
Ans: B
Let x, y, and z be the work done by X, Y, and Z in one day, respectively. x + y = 1/12 y + z = 1/15 x + z = 1/20 Adding the three equations: 2(x + y + z) = 1/12 + 1/15 + 1/20 = (5 + 4 + 3)/60 = 12/60 = 1/5 x + y + z = 1/10 Since y + z = 1/15, then x = 1/10 – 1/15 = (3 – 2)/30 = 1/30 Therefore, X alone takes 30 days to complete the task.
Q.19 A car travels from city A to city B at a speed of 40 km/hr and returns from city B to city A at a speed of 60 km/hr. What is the average speed of the car for the entire journey?
Check Solution
Ans: B
Average speed = (2 * Speed1 * Speed2) / (Speed1 + Speed2) = (2 * 40 * 60) / (40 + 60) = 4800 / 100 = 48
Q.20 The children ______ playing in the park when it started to rain.
Check Solution
Ans: C
The subject “children” is plural, so the verb must be plural.
Q.21 The company is planning _______ a new marketing strategy.
Check Solution
Ans: A
The correct idiom is “planning to develop”.
Q.22 The success of the project depends ______ the team members collaborate effectively.
Check Solution
Ans: B
The phrase “depends on” is typically followed by “whether” to introduce a conditional clause.
Q.23 Find the number which can replace the Question Mark: 7, 26, 63, 124, ?
Check Solution
Ans: A
The pattern is n^3 – 1. 7 = 2^3 – 1 26 = 3^3 – 1 63 = 4^3 – 1 124 = 5^3 – 1 Therefore, the next number is 6^3 – 1 = 215.
Q.24 The company will announce the new project ______ the market conditions improve.
Check Solution
Ans: A
This sentence indicates a conditional statement. The project announcement depends on the improvement of market conditions. “If” introduces the condition.
Q.25 The detective was able to ______ the criminal’s alibi with the evidence he had collected.
Check Solution
Ans: C
The detective would be trying to prove the alibi wrong.
Q.26 The rapid advancement in artificial intelligence promises to revolutionize numerous industries, leading to significant changes in the job market and prompting crucial discussions about ethical considerations and responsible ______ of AI technologies.
Check Solution
Ans: B
The context requires a word that describes the practical application and implementation of AI. Deployment fits this description best.
Q.27 A father is currently four times as old as his son. In 10 years, the father will be twice as old as his son. How old will the son be in 5 years?
Check Solution
Ans: A
Let the father’s current age be ‘f’ and the son’s current age be ‘s’. We have f = 4s. In 10 years, f + 10 = 2(s + 10). Substituting f = 4s, we get 4s + 10 = 2s + 20, which gives 2s = 10, so s = 5. The son’s age in 5 years will be 5 + 5 = 10.
Q.28 What is the present age of Sarah?
Statements:
Sarah is 10 years older than her brother.
Sarah’s brother is 5 years younger than their sister, who is currently 20 years old.
Check Solution
Ans: B
Statement I is insufficient as we don’t know the brother’s age. Statement II is sufficient because the sister is 20, and the brother is 15 (20-5). Sarah is then 25 (15+10).
Q.29 What is the age of Rohan?
Statements:
Rohan is 5 years older than his sister.
The combined age of Rohan and his sister is 35 years.
Check Solution
Ans: B
Both statements are needed to find the age of Rohan. Let Rohan’s age be R and sister’s age be S. From statement I, R = S + 5. From statement II, R + S = 35. Solving these equations, we get R = 20.
Q.30 What is the age of John?
Statements:
John is 5 years older than Mary.
The combined age of John and Mary is 35.
Check Solution
Ans: D
Statement I alone is not sufficient, as Mary’s age is unknown. Statement II alone is not sufficient, as their individual ages are unknown. Combining both, we can solve for John’s age. Let John’s age be J and Mary’s age be M. J = M + 5 and J + M = 35.
Q.31 To improve customer satisfaction, businesses often focus on providing ______ service.
Check Solution
Ans: A
Businesses aim to provide service that is quick and effective.
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