Q1. A boat goes 24 km upstream and 28 km downstream in 6 hours. It goes 30 km upstream and 21 km downstream in 6 hours and 30 minutes. The speed of the stream is:
(a) 10 km/h
(b) 5 km/h
(c) 4 km/h
(d) 6 km/h
(e) None of these
Q2. A train passes two bridges 104 m and 194 m long in 12 seconds and 18 seconds respectively. Find the speed of the train.
(a) 16 kmph
(b) 72 kmph
(c) 27 kmph
(d) 54 kmph
(e) None of these
Q3. In nut and bolts factory, one machine produces only nuts at the rate of 100 nuts per minute and need to be cleaned for 5 minutes after production of 1000 nuts. Another machine produces only bolts at the rate of 75 bolts per minute and need to be cleaned for 10 minutes after production of every 1500 bolts. If both the machine start production at the same time, what is the minimum duration required for producing 9000 pairs of nuts and bolts?
(a) 150 minutes
(b) 170 minutes
(c) 200 minutes
(d) 180 minutes
(e) None of these
Q4. A and B start at the same time from two ends S and T, at speeds of 7 m/sec and 11 m/sec towards each other, ST being 54 m. After reaching the opposite ends, they retrace their path and start moving towards each other. Find the total distance travelled by A when he meets B for the second time.
(a) 63 m
(b) 55 m
(c) 75 m
(d) 70 m
(e) None of these
Q5. A leak was found in a ship when it was 77 km from the shore. It was found that the leak admits 2.25 tonnes of water in 5.5 minutes. 92 tonnes will suffice to sink the ship. But the pumps can throw out the water at the rate of 12 tonnes an hour. Find the average rate of sailing at which the ship may reach the shore as it begins to sink.
(a) 9.75 km/h
(b) 13 km/h
(c) 14.5 km/h
(d) 10.5 km/h
(e) None of these
Q6. The driver of a car driving at the rate of 36 kmph locates a bus 40 meters ahead of him. After 20 seconds the bus is 60 meters behind. The speed of the bus is
(a) 36 kmph
(b) 20 m/sec.
(c) 72 m/sec.
(d) 18 kmph
(e) None of these
Q7. A takes a certain time to go downstream on a river between two villages. He takes 7 times as much time to cover the same distance upstream. What is the speed of the stream, if the distance between the villages is 60 km, which can be covered in 5 hours if the boat travels in still water?
(a) 18 kmph
(b) 5 kmph
(c) 9 kmph
(d) 8 kmph
(e) None of these
Q8. Local trains leave from a station at an interval of 15 minute at a speed of 16 km/h. A man moving from opposite side meets the trains at an interval of 12 minutes. Find the speed of the man.
(a) 4 km/h
(b) 3.5 km/h
(c) 4.5 km/h
(d) 5 km/h
(e) None of these
Q9. Three friends A, B and C live in Patiputra. They want to go to see the neighboring city Kalinga which is 150 km away from Patiputra but they have only one bike which can move at the speed of 40 km/hr. Each one of them can walk at the speed of 8 km/hr. (Only two people can travel by the bike at a time) What is the minimum time taken to reach to Kalinga if they used the best way to go.
(a) 6 hrs
(b) 7 hrs
(c) 7.5 hrs
(d) 8.5 hrs
(e) None of these
Q10. In a race of 800 m, L beats M by 45 seconds and beats N by 150 m. If M and N run a 800 m race, M beats N by 45 seconds. Find the time taken (in seconds) by M to run the race.
(a) 870
(b) 214
(c) 217.5
(d) 435
(e) None of these
ANSWERS :
S9. Ans.(c)
Sol. The objective of the problem is to minimize time taken by A, B and C to reach Kalinga by using the available resources. Let A & B start on bike and C starts walking towards Kalinga and A, leaves ‘B’ x km before Kalinga, so that he can cover this distance in exactly same time in which ‘A’ will go back to ‘C’ and bring him to Kalinga on bike.
Minimum time required can be derived:
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