TRAINS SET 1

Q.1 There are 3 trains from Mumbai to Ahmedabad and 7 trains from Ahmedabad to Kutch. In how many ways can Jethalal reach Kutch?

A) 18 ways

B) 19 ways

C) 20 ways

D) 21 ways

Ans. D

From Mumbai to A’bad, Jethalal can go in 3 ways. (Because there are three train, he can pick anyone)
Similarly From A’bad to Kutch, he can go in 7 ways.
Total ways: simple multiplication =3 ways x 7 ways =21 ways Jethalal can reach Kutch.

Q.2 A train travels at a certain average speed for a distance of 63 km and then travels a distance of 72 km at an average speed of 6 km/hr more than its original speed. If it takes 3 hours to complete the total journey, what is the original speed of the train in km/hr?
A) 24
B) 33
C) 42
D) 66
Ans. C
Let the original speed of the train in km/hr.
Then as per question,
T1 +t2 =63/x+72/x+6
3= 63(x+6) +72x/ x(x+6)
X(x+6)=21(x+6)+24x
X2+6x = 21x + 126 +24x
X2+6x-45x-126=0
X2-39-126 =0
Thus on solving, we get
(x-42) (x+3)=0
Therefore, x=42 Ans.

Q.3 A train which travels at the uniform rate of 10m a second leaves Madras for Arconum at 7:00 am. At what distance from Madras will it meet a train which leaves Arconum for Madras at 7:20 am & travels 1/3rd faster than the former does, the distance from Madras to Arconum being 68 km ?
A) 36 km
B) 47 km
C) 38 km
D) 42 km
Ans. A
S1= 10*18/5 = 36km/hr
S2 = 36+36/3 = 48 km/hr
Thus, Difference in time = T1 – T2 = 7 am – 7:20 am = -1/3 hr
Therefore distance of meeting point from Madras,
= 36+ [68-48 ( -1/3 ) / 36+48 ]=36 [68+16 / 36+48 ]= 36km/hr

Q.4 Suppose the telegraph poles on a railroad are 50 metres apart , how many will be passed by a car in 4hrs if the speed of the train is 45 km/hr ?
A) 3814
B) 4221
C) 3211
D) 3601
Ans. D
Total distance covered by the train = 4*45 = 180km
Therefore, in the distance of 180 km , there will be :
180000 / 50 + 1 = 3601 poles

Q.5 A train travels at a certain average speed for a distance of 63 km. Thereafter it travels a distance of 72 km with an average speed of 6 km/hr more than the original speed. Total time taken to complete the journey is 3 hours. What is the original average speed of the train ?
A) 48 km/hr
B) 36 km/hr
C) 54 km/hr
D) 42 km/hr
Ans. D