Next CSE-PPT: 14 March 2027 · Professional & Subprofessional
Civil Service Exam numerical ability reviewer on work and rate problems (workers, pipes, typists) and motion problems (speed, distance, time, average speed, meeting and catching up, current).
Work and motion problems use the same idea: amount = rate × time. For work, add the rates of people working together (or subtract a draining pipe); for motion, add speeds when objects move towards or away from each other, and subtract when one catches up with another.
Every answer in this set was calculated and checked by script. Calculators are not allowed in the Civil Service Exam, so practise each item on paper and look for the shortcut shown in the explanation.
Correct answer: A. 2 days
Ana does 1/6 of the task per day and Ben 1/3 (= 2/6). Together they do 3/6 = 1/2 per day, so they need 2 days. The combined time is always less than the faster worker's time.
Read detailsCorrect answer: A. 3 hours
Rates: 1/4 + 1/12 = 3/12 + 1/12 = 4/12 = 1/3 of the tank per hour, so both pipes take 3 hours. Adding the times (16 hours) or averaging them (8 hours) are common errors.
Read detailsCorrect answer: B. 15 days
Together they do 1/6 per day and Carlo does 1/10. Dina's rate = 1/6 − 1/10 = 5/30 − 3/30 = 2/30 = 1/15, so she would take 15 days alone.
Read detailsCorrect answer: D. 12
The project needs 8 × 15 = 120 worker-days. To finish in 10 days: 120 ÷ 10 = 12 workers. Fewer days require more workers, so this is inverse variation.
Read detailsCorrect answer: A. 3 hours
Each typist types 100 ÷ (5 × 2) = 10 pages per hour. Three typists type 30 pages per hour, so 90 pages take 90 ÷ 30 = 3 hours.
Read detailsCorrect answer: D. 18 hours
The net rate is 1/6 − 1/9 = 3/18 − 2/18 = 1/18 of the tank per hour, so it takes 18 hours. The drain works against the inlet, so its rate is subtracted.
Read detailsCorrect answer: C. 80 km/h
2 hours and 15 minutes is 2.25 hours. Speed = 180 ÷ 2.25 = 80 km/h. Writing 2 hours 15 minutes as 2.15 hours is a common mistake: 15 minutes is a quarter of an hour.
Read detailsCorrect answer: D. 3 hours
Time = distance ÷ speed = 210 ÷ 70 = 3 hours. Check: 70 km/h for 3 hours covers 210 km. The three forms of the formula are distance = speed × time, speed = distance ÷ time, and time = distance ÷ speed.
Read detailsCorrect answer: B. 30 km
40 minutes is 2/3 of an hour, so distance = 45 × 2/3 = 30 km. Multiplying 45 by 40 without converting minutes to hours gives a meaningless result.
Read detailsCorrect answer: D. 48 km/h
Take a distance of 120 km each way: going takes 2 hours and returning takes 3 hours. Average speed = 240 km ÷ 5 h = 48 km/h, not the simple average of 50, because more time is spent at the slower speed.
Read detailsCorrect answer: C. 360 km
Moving in opposite directions, the distance between them grows at 50 + 70 = 120 km per hour. After 3 hours they are 120 × 3 = 360 km apart.
Read detailsCorrect answer: C. 3 hours
Moving towards each other, they close the gap at 60 + 40 = 100 km per hour. They meet after 300 ÷ 100 = 3 hours. In that time, the faster bus covers 180 km and the slower one 120 km, which add up to 300 km.
Read detailsCorrect answer: B. 2 hours
By 9:00 a.m. the van is 40 km ahead. The car gains 60 − 40 = 20 km each hour, so it catches up after 40 ÷ 20 = 2 hours, at 11:00 a.m.
Read detailsCorrect answer: B. 20 m/s
Multiply by 1,000 to get metres and divide by 3,600 to get seconds: 72 × 1,000 ÷ 3,600 = 20 m/s. A shortcut is to multiply km/h by 5/18.
Read detailsCorrect answer: A. 10 seconds
72 km/h = 20 m/s. To pass a post, the train must travel its own length: 200 ÷ 20 = 10 seconds. To pass a platform or bridge, the train would have to cover its own length plus the length of the platform.
Read detailsCorrect answer: D. 24 minutes
Time = 2 ÷ 5 = 0.4 hour, and 0.4 × 60 = 24 minutes. Alternatively, 5 km per hour means 1 km every 12 minutes, so 2 km take 24 minutes.
Read detailsCorrect answer: B. 15 days
In 4 days Ella completes 4/12 = 1/3 of the job, leaving 2/3. Fred does 2/3 in 10 days, so the whole job would take him 10 ÷ 2/3 = 15 days.
Read detailsCorrect answer: D. 18 days
The job takes 3 × 6 = 18 painter-days, so one painter needs 18 days. Dividing 6 by 3 (2 days) is the opposite of the correct reasoning.
Read detailsCorrect answer: A. 2 hours
Downstream, the current adds to the boat's speed: 15 + 3 = 18 km/h. Time = 36 ÷ 18 = 2 hours. Upstream, the speed would be 15 − 3 = 12 km/h, taking 3 hours.
Read detailsCorrect answer: A. 25 minutes
Time = 1,000 ÷ 40 = 25 minutes. Rate problems all use the same idea: amount of work = rate × time. Check: 25 minutes × 40 pages per minute = 1,000 pages.
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