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# Maths Questions for CTET Exam : 4th september 2018 (solutions)

Q1.A train travels a distance of 600 km at a constant speed. If the speed of the train is increased by 5 km/hr, the journey would take 4 hrs less. Find the speed of the train.
(a) 100 km/hr
(b) 25 km/hr
(c) 50 km/hr
(d) 75 km/hr
Q2. A train covers 180 km distance in 4 hours. Another train covers the same distance in 1 hour less. What is the difference in the distances covered by these trains in one hour if they are moving in the same direction?
(a) 45 km
(b) 9 km
(c) 40 km
(d) 15 km
Q3. A man can swim 48 m/min in still water, he swims 200 m against the current and 200 m with the current. If the difference between those two times is 10 min, what is the speed of the current?
(a) 30 m/min
(b) 31 m/min
(c) 29 m/min
(d) 32 m/min
Q4. A motorboat went downstream for 28 km and immediately returned. It took the boat twice as long to make the return trip. If the speed of the river flow were twice as high, the trip downstream and back would take 672 minutes. Find the speed of the boat in still waster and the speed of the river flow.
(a) 9 km/hr, 3 km/hr
(b) 9 km/hr, 6 km/hr
(c) 8 km/hr, 2 km/hr
(d) None of these
Q5. Two trains pass each other on parallel lines. Each train is 100 metres long. When they are going in the same direction, the faster one takes 60 seconds to pass the other completely. If they are going in opposite directions they pass each other completely in 10 seconds. Find the speed of the slower train in km/hr.
(a) 30 km/hr
(b) 42 km/hr
(c) 48 km/hr
(d) 60 km/hr
Q6.Train A starts its journey from Patna to Hazipur while train B starts from Hazipur to Patna. After crossing each other they finish their journey in 81 hours and 121 hours respectively. Then what will be speed of train B if train A speed is 44 km/h?
(a)44 Km/h
(b)55 Km/h
(c)36 Km/h
(d)None of these
Q7. A man can row 7 km/hr in still water. If the river is running at 3 km/hr, it takes 6 hours more in upstream than to go downstream for the same distance. How far is the place?
(a)48 km
(b)36 km
(c)42 km
(d)40 km
Q8. Gourav fires two bullets from the same place at an interval of 15 minutes but Rohit sitting in a train approaching the place hears the second sound 14 minutes  30 seconds after the first. What is the approximate speed of train (if sound travels at the speed of 330 meter per second)?
(a)330/23 m/sec
(b)330/29 m/sec
(c)330/27 m/sec
(d)330/31 m/sec

Q9. In a circus there was a leopard and a tiger walking in two different rings of same radii. There I observed that when leopard moved 3 steps, tiger moved 5 steps in the same time, but the distance traversed by leopard in 5 steps in equal to the distance traversed by tiger in 4 steps. What is the number of rounds that a leopard made when tiger completed 100 rounds
(a) 120
(b) 48
(c) 75
(d) 80
Q10. A train leaves the station 1/2 hour before the scheduled time. The driver decreases its speed by 25 km/hr. At the next station 250 km away, the train reached on time. Find the original speed of the train.
(a) 100 km/hr
(b) 125 km/hr
(c) 200 km/hr
(d) 180 km/hr
Q11.Train – A crosses a stationary train – B in 45 seconds and a pole in 13 seconds with the same speed. The length of the train – A is 260 metres. What is the length of the stationary Train-B?
(a) 360 metres
(b) 260 metres
(c) 640 metres
(d) 460 metres
Q12.Three persons start walking together and their steps measure 40 cm, 42 cm and 45 cm respectively. What is the minimum distance each should walk so that each can cover the same distance in complete steps?
(a)25.2 m
(b)25.4 m
(c)25.8 m
(d)26 m

Q13. A train crosses a platform and a tunnel in 18 and 32 seconds respectively. The speed of the train and length of the train are 45 kmph and 140 metres respectively. Find the length of platform is approximately what percent less than the length of tunnel?
(a) 72%
(b) 67%
(c) 82%
(d) 61%
Q14. A 200 m long train passes a cycler, running in the same direction at 12 km/hr, in 10 second and a car travelling in the same direction in 15 s. At what speed is the car travelling (length of both the cycler and car is negligible)?
(a) 36 km/hr
(b) 30 km/hr
(c) 34 km/hr
(d) 32 km/hr
Q15. Two trains, 100 km apart, travel towards each other on the same track. One train travels at 40 km/hr; the other travels at 60 km/hr. A bird starts flying at a speed of 90 km/hr, at the same location of the faster train. When it reaches the slower train, it turns around and flies in the opposite direction at the same speed. When it reaches the faster train, again it turns around and so on. When the two trains collide, how much distance has the bird flown?
(a) 90 km
(b) 45 km
(c) 180 km
(d) 135 km

Solutions
S1. Ans.(b)
Sol.
Using formula,
S(S+5)/5×4=600
S(S+5)=750=25 (25+5)
Speed of the train = 25 km/hr
Alternately,
600/s-600/(s+5)=4
(600s+3000-600s)/s(s+5) =4
s=25 km/hr
S2. Ans.(d)
Sol. First train speed = 45 km/hr
2nd train speed = 60 km/hr
∴Differencein distance covered in 1 hr = 15 km
S3. Ans.(d)
Sol. 200/(48-V)-200/(48+V)=10
Or, 20(48 + V) – 20(48 – V) = 〖48〗^2-V^2
Or, V^2+40V-2304=0
Or, V = 32 m/min.
S4. Ans.(a)
Sol.
Let speed boat =x km/h
Let speed of stream = y km/h
Condition I
2×28/(x+y)=28/(x-y)⇒x/y=3/1
Condition II
28/((3y+2y) )+28/((3y-2y) )=672/60
⇒28/5y+28/y=672/60
⇒(28+28×5)/5y=672/60⇒y=3 kmph
∴x=9 kmph
S5. Ans.(a)
Sol.
Let speed of faster train = x km/h
Let speed of slower train = y km/h
When both move in same direction =60/(60×60)=2/(x-y)
When both move in opposite direction =10/(60×60)=2/(x+y)
x+y=72
x=42 km/h
y=30 km/h
S6. Ans.(c)
Sol.
Let Speed of train B = v km/hr
Total distance = (x + y) km
Distance covered by train A in 81 hours = y km
⇒ y = 44 × 81
= 3564 km … (i)
& Distance covered by train B in 121 hours = x km
⇒ 121 v = x km …(ii)
But x/44=y/v
⇒x=44y/v
⇒x=(44×3564)/v…(iii)
From (ii) and (iii)
121v² = 44 × 3564
⇒ v = 36 km/hr
S7. Ans.(d)
Sol. x = 7 km/h
y = 3 km/hr
d/(7-3)=6+d/10
d = 40 km
S8. Ans.(b)
Sol.
Clearly,
Sound of 2nd gunshot will take 30 seconds to cover the distance which will be equal to the distance between the two
Hence
Speed of train =(330 m/sec⁡×30 sec)/((14×60+30))
=(330×30)/870=330/29  m/sec
S9. Ans.(b)
Sol.
The ratio of speeds = The ratio of distances, when time is constant.
Given that 5L=4T
Or, 1L=4/5 T
In a fixed time, distance travelled by leopard =3×4/5 T=12/5 T
And distance travelled by tiger is 5T
∴ The ratio of distances covered by leopard to the tiger = 12 : 25
Again, ratio of rounds made by leopard to the tiger = 12 : 25
Hence, leopard makes 48 rounds, when tiger makes 100 rounds.
S10. Ans.(b)
Sol.
Let original speed of the train was x km/hr.
And original time was t hours
∴x(t-1/2)=(x-25)t
⇒ t=x/50
also x(t-1/2)=250
∴x(x/50-1/2)=250
⇒x^2-25x-12500=0
⇒(x-125)(x+100)=0
⇒x=125 km/hr
S11. Ans.(c)
Sol. Speed of train A = 260/13
= 20 m/sec
∴ Length of train B = 45 × 20 – 260
= 640 m
S13. Ans.(b)
Sol.
Speed of train (in m/s) = 45×5/18 = 25/2
Length of platform = 18×25/2-140
= 85 m
Length of tunnel = 32×25/2-140
= 260 m
∴ Required percentage = (260-85)/260×100
= 67%
S15. Ans.(a)
Sol.
Since the trains are 100 km apart, and the trains are travelling towards each other at 40 and 60 km/hr, the trains will collide in one hour. The bird must be flying at 90 k/hr during this time, so the bird travels 90 km.