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Time and Distance - Aptitude Questions and Answers - RejinpaulPlacement




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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.
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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?
Answer & Solution
Answer: b) 11 : 9
Solution:   In the same time, they cover 110 km and 90 km respectively.

Ratio of their speeds = 110 : 90 = 11 : 9.
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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]
Answer & Solution
Answer: d) 900 km

Solution:   At the time of meeting, let the distance travelled by the second train be x km.

Then, distance covered by the first train is (x + 100) km.

x/40 = (x + 100) / 50
50x = 40x + 4000
X = 400.

So, distance between P and Q = (x + x + 100) km = 900 km.
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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?
Answer & Solution
Answer: c) 480 km

Solution:   Suppose they meet x hours after 14.30 hrs.

Then, 60x = 80 (x - 2) or x = 8.

Required distance = (60 * 8) km = 480 km.
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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.
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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.
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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]
Answer & Solution
Answer: b) 10 min

Solution:   Due to stoppages, it covers 9 km less.

Time taken to cover 9 km = [(9/54) * 60] min = 10 min.
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