


57.
Two cars P and Q start at the same time from A and B which are 120 km apart. If the two cars travel in opposite directions, they meet after one hour and if they travel in same direction (from A towards B), then P meets Q after 6 hours. What is the speed of car P? [S.B.I.P.O. 2000]
Answer & Solution
Answer: b) 70 kmph
Solution: Let their speeds be x kmph and y kmph respectively. Then, 120 / (x + y) = 1 => x + y = 120 ........ (i) Now, when they move in same direction. : (Distance travelled by P in 6 hrs)  (Distance travelled by Q in 6 hrs) = 120 km. => 6x  6y = 120 => x  y = 20 ....... (ii) Solving (i) and (ii), x = 70, y = 50. P's speed = 70 kmph. 58.
Two trains starting at the same time from two stations 200 km apart and going in opposite directions cross each other at a distance of 110 km from one of the stations. What is the ratio of their speeds?
59.
Two trains start from P and Q respectively and travel towards each other at a speed of 50 km/hr and 40 km/hr respectively. By the time they meet, the first train has travelled 100 km more than the second. The distance between P and Q is : [S.S.C 2000]
60.
Bombay Express left Delhi for ?Bombay at 14.30 hrs, travelling at a speed of 60 kmph and Rajdhani Express left Delhi for Bombay on the same day at 16.30 hrs, travelling at a speed of 80 kmph. How far away from Delhi will the two trains meet?
61.
A train M leaves Meerut at 5 a.m. and reaches Delhi at 9 a.m. Another train leaves Delhi at 7 a.m. and reaches Meerut at 10.30 a.m. At what time do the two trains cross each other?
Answer & Solution
Answer: b) 7.56 a.m.
Solution: Let the distance between Meerut and Delhi be x km and let the train meet y hours meet y hours after 7 a.m. Clearly, M covers x km in 4 hrs and N covers x km in (7/2) hrs Speed of M = x/4 kmph Speed of N = 2x/7 kmph. [Distance covered by M in (y + 2) hrs ] + [Distance covered by y hrs = x. x/4 (y + 2) + (2x/y) * y = x => (y + 2)/4 + (2y/7) = 1 => y = 14/15 hrs =[(14/15) * 60] min = 56 min. Hence, the trains meet at 7.56 a.m. 62.
A man takes 5 hours 45 min. in walking to a certain place and riding back. He would have gained 2 hours by riding both ways. The time he would take to walk both ways, is:
Answer & Solution
Answer: c) 7 hrs 45 min
Solution: Let the distance be x km. (Time taken to walk x km) + (Time taken to ride x km) = 23/4 hr. => (Time taken to walk 2x km) + (Time taken to ride 2x km) = 23/2 hrs. But, time taken to ride 2x km = 15/4 hrs. Time taken to walk 2x km = [(23/2)  (15/4)] hrs = 31/4 hr = 7 hrs 45 min. 63.
Excluding stoppages, the speed of a bus is 54 kmph and including stoppages, it is 45 kmph. For how many minutes does the bus stop per hour? [N.I.F.T 2002]
