11 questionswith explanationsfor RAS, Patwari, VDO and other Rajasthan exams
A 300 m long train passes completely over a 450 m long platform in 30 seconds. Find the speed of the train in km/h.
Answer: (1) 90 km/h
Explanation
Distance = 300 + 450 = 750 m in 30 s = 25 m/s; 25 × 18/5 = 90 km/h.
Priya covers three equal distances at speeds of 30 km/h, 40 km/h and 60 km/h respectively. What is her average speed for the whole journey?
Answer: (1) 40 km/h
Explanation
Take each distance as 120 km: times are 4 h, 3 h and 2 h. Average speed = 360 ÷ 9 = 40 km/h (not the simple average 43 1/3).
Working alone, Arjun would paint a house in 12 days and Bhanu in 18 days. After painting together for 4 days, Arjun goes away. How many more days will Bhanu need to finish the painting?
Answer: (2) 8 days
Explanation
Together they do 1/12 + 1/18 = 5/36 per day; in 4 days 20/36 is done. The remaining 16/36 = 4/9 takes Bhanu 4/9 × 18 = 8 days.
Pipes A and B can fill a tank in 4 hours and 12 hours respectively, and pipe C can empty the full tank in 8 hours. If all three pipes are opened together on an empty tank, in how much time will the tank be filled?
Answer: (3) 4 h 48 min
Explanation
Net filling per hour = 1/4 + 1/12 − 1/8 = (6 + 2 − 3)/24 = 5/24, so time = 24/5 h = 4 h 48 min.
Two runners start together from one point of a 400 m circular track and run in the same direction at 5 m/s and 3 m/s. After how many seconds will the faster first meet the slower?
Answer: (2) 200 s
Explanation
On a circular track running the same way, the faster runner must gain one full lap on the slower one. Relative speed = 5 − 3 = 2 m/s, so time = 400/2 = 200 s. Check: in 200 s they run 1,000 m and 600 m, which differ by exactly 400 m. The value 50 s = 400/(5 + 3) applies when the runners go in opposite directions, so it is wrong here.
12 men can build a wall in 18 days. After they have worked for 6 days, 6 more men join them. In how many more days will the wall be completed?
Answer: (3) 8 days
Explanation
Work in man-days: total = 12 × 18 = 216. In 6 days 12 men do 72, leaving 144. With 12 + 6 = 18 men, the rest takes 144/18 = 8 days. Check: 72 + 18 × 8 = 216. Dividing by 12 only (144/12 = 12 days) is wrong because it ignores the 6 extra men who join.
Towns P and Q are 380 km apart. A bus leaves P at 8 a.m. towards Q at 50 km/h and another bus leaves Q at 9 a.m. towards P at 60 km/h. At what time do the two buses meet?
Answer: (1) 12 noon
Explanation
By 9 a.m. the first bus has covered 50 km, leaving 330 km. The buses then close in at 50 + 60 = 110 km/h, so they meet after 330 / 110 = 3 hours, at 12 noon. Dividing the full 380 km by 110 gives about 3.45 hours, which wrongly ignores the one-hour head start.
6 men can finish a piece of work in 15 days and 9 women can finish it in 20 days. In how many days will 6 men and 6 women together finish it?
Answer: (4) 10
Explanation
One man does 1/90 of the work a day and one woman 1/180. Six men and six women do 6/90 + 6/180 = 1/10 a day, so they need 10 days. The value 15 would be the time for the 6 men alone, ignoring the women.
A, B and C can finish a piece of work alone in 12, 24 and 8 days respectively. All three start together, and C leaves after 2 days. In how many days in all is the work finished?
Answer: (1) 6
Explanation
Together they do 1/12 + 1/24 + 1/8 = 1/4 of the work a day, so 2 days finish 1/2. A and B do 1/12 + 1/24 = 1/8 a day, so the other half takes 4 days: total 2 + 4 = 6 days. 4 is only the remaining time.
A cyclist goes to a village at 12 km/h and returns by the same road at 8 km/h. If the whole journey takes 5 hours, how far is the village?
Answer: (3) 24 km
Explanation
If the distance is d km, d/12 + d/8 = 5, so 5d/24 = 5 and d = 24 km. Using the simple mean speed 10 km/h for 5 hours gives 50 km, which is wrong because the two legs take different times.
An inlet pipe can fill a tank in 12 hours and an outlet pipe can empty the full tank in 20 hours. If both are opened together when the tank is empty, in how many hours will the tank be full?
Answer: (3) 30 hours
Explanation
Net filling in one hour = 1/12 − 1/20 = 1/30 of the tank, so it fills in 30 hours. 8 is only 20 − 12, and 32 wrongly adds the two times.