Question 1

A train 200m long crosses a platform 300m long in 25 seconds. Find its speed.

Accepted Answer

Total distance = train length + platform length = 200 + 300 = 500m. Time = 25 seconds. Speed = 500/25 = 20 m/s = 20 × 18/5 = 72 km/hr. Key formula: Speed = (Length of train + Length of object) / Time.

Question 2

If A can do a job in 12 days and B in 15 days, how long will they take working together?

Accepted Answer

A's rate = 1/12, B's rate = 1/15. Combined rate = 1/12 + 1/15 = 5/60 + 4/60 = 9/60 = 3/20. Time = 20/3 = 6.67 days ≈ 6 days 16 hours. Formula: Time = (A×B)/(A+B) = (12×15)/(12+15) = 180/27 = 20/3 days.

Question 3

In how many ways can 5 people be seated in a row?

Accepted Answer

5! = 5 × 4 × 3 × 2 × 1 = 120 ways. If seated in a circle: (5-1)! = 24 ways (fix one person, arrange rest). If only 3 seats: P(5,3) = 5!/(5-3)! = 60 ways.

Question 4

A bag contains 3 red, 5 blue, and 2 green balls. What is the probability of picking 2 blue balls?

Accepted Answer

Total balls = 10. P(2 blue) = C(5,2)/C(10,2) = 10/45 = 2/9 ≈ 0.222. Using combinations: C(5,2) = 10, C(10,2) = 45. If with replacement: (5/10) × (5/10) = 1/4 = 0.25.

Question 5

Complete the series: 2, 6, 12, 20, 30, ?

Accepted Answer

Differences: 4, 6, 8, 10, … (increasing by 2). Next difference = 12. Answer = 30 + 12 = 42. Alternative pattern: n(n+1) where n = 1,2,3,4,5,6 → 2, 6, 12, 20, 30, 42.

Question 6

Two pipes fill a tank in 12 and 16 hours. A drain empties it in 24 hours. How long to fill with all open?

Accepted Answer

Rate: 1/12 + 1/16 - 1/24 = 2/24 + 1.5/24 - 1/24 = 2.5/24. Using LCM(12,16,24) = 48: Pipe1 fills 4/hr, Pipe2 fills 3/hr, Drain empties 2/hr. Net = 5 units/hr. Time = 48/5 = 9.6 hours.

Aptitude & Reasoning Questions with Answers

1A train 200m long crosses a platform 300m long in 25 seconds. Find its speed.

2If A can do a job in 12 days and B in 15 days, how long will they take working together?

3In how many ways can 5 people be seated in a row?

4A bag contains 3 red, 5 blue, and 2 green balls. What is the probability of picking 2 blue balls?

5Complete the series: 2, 6, 12, 20, 30, ?

6Two pipes fill a tank in 12 and 16 hours. A drain empties it in 24 hours. How long to fill with all open?

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