Q1. A train covers a distance A and B in 45 minutes. If the speed is decreased by 5 km/hr, then it takes 48 minutes to cover the same distance. Find the distance between A and B (in km.) and the speed of a train?
(a) 60 km, 75 km/hr
(b) 60 km, 80 km/hr
(c) 40 km, 80 km/hr
(d) 70 km, 75 km/hr
Q2.A train covers a distance between A and B in 48 minutes. The another train having speed 6 km/hr. less than the first train covers the distance B to A in 60 minutes. Find the distance between A and B?
(a) 24 km
(b) 48 km
(c) 40 km
(d) 15 km
Q3. The speed of two trains are in the ratio 7 : 9. They are moving in the opposite directions on parallel tracks. The first train crossed a telegraph pole in 4 seconds whereas the second train crossed the same pole in 6 seconds. Find the time taken by the train to cross each other completely.
(a) 2 1/6seconds
(b) 3 1/6seconds
(c) 4 2/8seconds
(d) 5 1/8seconds
Q5. A book vendor sold a book at a loss of 20%. Had he sold it for Rs. 108 more, he would have earned a profit of 30%. Find the cost price of the book?
(a) Rs. 216
(b) Rs. 648
(c) Rs. 240
(d) Rs. 432
Q6. The greatest number which can divide 1356, 1868 and 2764 leaving the same remainder 12 in each case is:
Q7. A motorcyclist goes from Mumbai to Pune, a distance of 192 km at an average speed of 32 km/h. Another man starts from Mumbai by car, 2 1/2 hours after the first and reaches Pune half an hour earlier. What is the rate of the speed of the motorcycle and the car?
(a) 1 : 2
(b) 1 : 3
(c) 10 : 27
(d) 5 : 4
Q8. A person sets to cover a distance of 12 km in 45 minutes. If he covers 3/4 of the distance in 2/3rd time, what should his speed to cover the remaining distance in the remaining time?
(a) 16 km/hr
(b) 8 km/hr
(c) 12 km/hr
(d) 14 km/hr
Q9. Length of a train is 287 m and it passes a bridge in 38 sec at the speed of 90 km/h. What is the length of the bridge?
(a) 665 m
(b) 663 m
(c) 680 m
(d) 580 m
Q10. A train running at certain speed crosses a stationary engine in 20 seconds. To find out the speed of the train, which of the following information is necessary?
(a) Only the length of the train
(b) Only the length of the engine
(c) Either the length of the train or the length of the engine
(d) Both the length of the train and the length of the engine
Sol. To solve such questions, we keep 99 as it is in second part, but in part first, we convert all 9’s into zeros.
y = Rs. 216
Required number = H.C.F of (1356 – 12), (1868 – 12) and (2764 – 12)
= H.C.F of 1344, 1856 and 2752 = 64.
Speed of the first man = 32 km/hr
Time taken = 192 ÷ 32 = 6 hr
Second man covers 192 km in 3 hr
∴ Speed of the second man
= 192 ÷ 3 = 64 km/hr
Ratio = 32 : 64 or 1 : 2
Distance already covered = (3/4) × 12 = 9 km
Time spent = (2/3) × 45 min = 30 min
Distance left = (12-9) km = 3 km
Time left = (45-30) min = 15 min
∴ Required speed =3/ (15/60) km/hr
= 12 km/hr
Total distance covered = 90 × (5/18) × 38 = 950 m
So, length of bridge = 950 – 287 = 663
Since the sum of the length of the train and the engine is needed, so both the lengths must be known.