BANK & INSURANCE (SPEED TIME AND DISTANCE) PART 3

Total Questions: 45

11. A thief break away from a police station situated in Shivpuri village towards Goa city at 4 a.m. with a speed of 50 km/hour. Police realised the breakdown at 6 a.m. and started chasing the thief with the speed of 70 km/hour. At what distance from Goa city, police will catch the thief if the distance between police station and Goa is 480 km?

Correct Answer: (c) 130 km
Solution:Distance travelled by thief when police realised the breakdown = 2 × 50 = 100 km
Time taken by police to chase the thief = 100 ÷ (70 − 50) = 5 hours
Distance travelled by Police = 5 × 70 = 350 km
Therefore, required distance = 480 − 350 = 130 km
Hence, option c.

12. Which of the following options can be used to fill the blank in order to make the given statement true?

The length of train A is 324 m and it crosses a pole in ___ seconds. Train B, whose length is 364 m crosses a ___ m long platform in 18 seconds while train A and train B can cross each other in 8.6 seconds while travelling in opposite directions.

The values given in which of the following options will fill the blanks in the same order in which is it given to make the statement true:
I. 7.2, 266  II. 12, 590
III. 9, 340  IV. 10.8, 536

Correct Answer: (c) Only I, II and IV 
Solution:

The length of train A = 324 m
The length of train B = 364 m

I. 7.2, 266
Speed of train A = 324 × 7.2 = 45 m/s
Let the speed of train B = x m/s

According to the question,
(45 + x) = (324 + 364)/8.6
387 + 8.6x = 688
8.6x = 301
x = 35

Speed of train B = 35 m/s

Time taken by train B to cross 266 m long platform
= {(266 + 364)/35}
= 630/35 = 18 seconds

This is satisfying the condition.

II. 12, 590
Speed of train A = 324/12 = 27 m/s
Let the speed of train B = x m/s

According to the question,
(27 + x) = (324 + 364)/8.6
232.2 + 8.6x = 688
8.6x = 455.8
x = 53

Speed of train B = 53 m/s

Time taken by train B to cross 590 m long platform
= {(590 + 364)/53}
= 954/53 = 18 seconds

This is satisfying the condition.

III. 9, 340
Speed of train A = 324/9 = 36 m/s
Let the speed of train B = x m/s

According to the question,
(36 + x) = (324 + 364)/8.6
309.6 + 8.6x = 688
8.6x = 378.4
x = 44

Speed of train B = 44 m/s

Time taken by train B to cross 340 m long platform
= {(340 + 364)/44}
= 704/44 = 16 seconds

This is not satisfying the condition.

IV. 10.8, 536
Speed of train A = 324/10.8 = 30 m/s
Let the speed of train B = x m/s

According to the question,
(30 + x) = (324 + 364)/8.6
258 + 8.6x = 688
8.6x = 430
x = 50

Speed of train B = 50 m/s

Time taken by train B to cross 536 m long platform
= {(536 + 364)/50}
= 900/50 = 18 seconds

This is satisfying the condition.

Hence, option c

13. Directions (13-14): Answer the questions based on the information given below.

Subhash started from point P in a boat to reach point Q. After 8.7 hours, he covered only 15% of the distance and reached at point R. Now, Subhash started from point R and reached at mid-point of P and Q and came back to R in 35.35 hours. Time taken by Subhash to cover the distance between Q and P when he started from Q is 13 hours more than time taken by Rajesh to cover a distance of 720 km in upstream and the speed of Rajesh in downstream is 20% more than his speed in still water.

Ques: In what time Subhash can cover the distance between Q and P if he started from point Q?

Correct Answer: (c) 43 hours
Solution:

(c): Let Subhash is going in upstream while going from point P to point Q.

According to question,
Subhash covers 15% distance in 8.7 hours

So, Subhash will cover 35% distance (R to mid-point of P and Q) in 8.7 × 7/3 = 20.3 hours

Time taken by Subhash to come back from mid-point to point R in upstream = 35.35 − 20.3 = 15.05 hours

35% distance is covered by Subhash in 15.05 hours

So, total distance will be covered in 15.05 × 100/35
= 43 hours

Speed of Rajesh in upstream = 720/(43 − 13)
= 720/30 = 24 km/h

Let speed of Rajesh in still water is ‘x’ km/h
Speed of Rajesh in downstream = 1.2x km/h

So, 0.8x = 24
x = 24/0.8 = 30 km/h

Speed of Rajesh in still water = 30 km/h

Speed of stream = (36 − 24)/2 = 6 km/h

Desired time = 43 hours.

Hence, option c.

14. Ques: Find the speed of stream?

Correct Answer: (d) 6 km/h 
Solution:

Let Subhash is going in upstream while going from point P to point Q

According to question,
Subhash covers 15% distance in 8.7 hours
So, Subhash will cover 35% distance (R to mid-point of P and Q) in 8.7 × 7/3 = 20.3 hours

Time taken by Subhash to come back from mid-point to point R in upstream = 35.35 − 20.3 = 15.05 hours

35% distance is covered by Subhash in 15.05 hours
So, total distance will be covered in 15.05 × 100/35
= 43 hours

Speed of Rajesh in upstream = 720/(43 − 13)
= 720/30 = 24 km/h

Let speed of Rajesh in still water is ‘x’ km/h
Speed of Rajesh in downstream = 1.2x km/h

So, 0.8x = 24
x = 24/0.8 = 30 km/h

Speed of Rajesh in still water = 30 km/h

Speed of stream = (36 − 24)/2 = 6 km/h
Speed of stream = 6 km/h

Hence, option d.

15. Directions (15-16): Study the following information carefully and answer the related questions.

The following information gives the data regarding the speed and length of trains A, B, C, and D.
Trains A and C cross a pole in 8.75 seconds and 6 seconds respectively. While moving in the same direction, train B crosses train A in 2 minutes 17.5 seconds. Train D crosses a 60 meters long bridge in 3.2 seconds less time than train A to cross the same bridge. Train B crosses a man running with a speed of 7.2 km/hr in opposite direction in 6.75 seconds. While moving in opposite direction, the relative speed of train A and train B is 34 m/s. Train C is 4 meters longer than train A. Train C crosses a platform in 10.5 seconds while train D takes 9 seconds to cross the half of length of the platform crossed by C.

Ques: If all the trains started moving from the same point to the same direction, then the fastest train will cross all other trains in ___ seconds.

Correct Answer: (c) 67.5
Solution:

We know, time taken = distance covered/speed
Let the speed of trains A, B, C, and D be ‘a’ m/s, ‘b’ m/s, ‘c’ m/s, and ‘d’ m/s respectively. Let lengths of trains A, B, C and D are p, q, r, and s meters respectively.

Trains A and C crosses a pole in 8.75 seconds and 6 seconds respectively. Then,
8.75 = p/a => p = 8.75a ……(i)
6 = r/c ……(ii)

Train B crosses a man running with a speed of 7.2 km/hr in opposite direction in 6.75 seconds.
7.2 km/hr = 7.2 × 5/18 m/s = 2 m/s

Since man and train B are running in the opposite direction. So, their relative speed = b + 2
And, 6.75 = q/(b + 2) => q = 6.75b + 13.5 ……(iii)

While moving in the same direction, train B crosses train A in 2 minutes 17.5 seconds. Then,
Train B is crossing train A and both are moving in the same direction. So, their relative speed = b − a
2 minutes 17.5 seconds = (2 × 60 + 17.5) seconds = 137.5 seconds

137.5 = (p + q)/(b − a) ……(iv)

While moving in opposite direction, relative speed of train A and train B is 34 m/s. So, their relative speed = a + b = 34
a = 34 − b ……(v)

From (i) and (v), we have
p = 8.75(34 − b) = 297.5 − 8.75b ……(vi)

From (iii), (iv), (v) and (vi), we have
137.5 = (297.5 − 8.75b + 6.75b + 13.5)/(b − (34 − b))

137.5 × (2b − 34) = 311 − 2b
275b − 4675 = 311 − 2b
277b = 4986
b = 18

a = 34 − 18 => a = 16

p = 8.75 × 16 => p = 140
q = 6.75 × 18 + 13.5 => q = 135

Train C is 4 meters longer than train A. Then,
r = p + 4 = 140 + 4 => r = 144

Now, from (ii), we get
6 = r/c
6 = 144/c => c = 24

Train C crosses a platform in 10.5 seconds while train D takes 9 seconds to cross the half of length of the platform crossed by C.

10.5 = (length of platform + r)/c
10.5 = (length of platform + 144)/24

Length of platform = 108

Now, 9 = (length of platform/2 + s)/d
9 = (108/2 + s)/d
s = 9d − 54 ……(vii)

Train D crosses a 60 meters long bridge in 3.2 seconds less time taken by train A to cross the same bridge.

Then, time taken by train A to cross a 60 meters long bridge = (p + 60)/a
= (140 + 60)/16 = 12.5 seconds

And time taken by train D to cross 60 meters long bridge = 12.5 − 3.2 = (60 + s)/d
= 9.3

d = 20

And s = 9 × 20 − 54 => s = 126

In tabular form:

Train

Speed in m/s

Length in meters

A

16

140

B

18

135

C

24

144

D

20

126

Order of trains according to their respective speeds:
C > D > B > A

So, C is the fastest train, and it will cross train A first, then train B and then train D. This means the time taken by train C to cross all other trains is equal to the time taken by it to cross the train D.

Since all trains are moving in the same direction from the same point. So, relative speed of train C and D = c − d = 24 − 20 = 4 m/s

Therefore, time taken by train C to cross all other trains = time taken by train C to cross train D
= (r + s)/relative speed of train C and D
= (144 + 126)/4 = 67.5 seconds

16. Length of train E is equal to the average length of trains B, C, and D. If train E can cross a 121 m long bridge in 16 seconds, then what is the respective ratio of speeds of train A to train E?

Correct Answer: (c) 1: 1
Solution:

We know, time taken = distance covered/speed
Let the speed of trains A, B, C, and D be ‘a’ m/s, ‘b’ m/s, ‘c’ m/s, and ‘d’ m/s respectively. Let lengths of trains A, B, C and D are p, q, r, and s meters respectively.

Trains A and C crosses a pole in 8.75 seconds and 6 seconds respectively. Then,
8.75 = p/a => p = 8.75a ……(i)
6 = r/c ……(ii)

Train B crosses a man running with a speed of 7.2 km/hr in opposite direction in 6.75 seconds.
7.2 km/hr = 7.2 × 5/18 m/s = 2 m/s

Since man and train B are running in the opposite direction. So, their relative speed = b + 2

And, 6.75 = q/(b + 2) => q = 6.75b + 13.5…(iii)
While moving in the same direction, train B crosses train A in 2 minutes 17.5 seconds. Then,
Train B is crossing train A and both are moving in the same direction. So, their relative speed = b - a
2 minutes 17.5 seconds = (2 × 60 + 17.5) seconds = 137.5 seconds
137.5 = (p + q)/(b - a)…(iv)
While moving in opposite direction, relative speed of train A and train B is 34 m/s. So, their relative speed = a + b = 34
a = 34 - b …(v)

From (i) and (v), we have
p = 8.75(34 - b) = 297.5 - 8.75b …(vi)

From (iii), (iv), (v) and (vi), we have
137.5 = (297.5 - 8.75b + 6.75b + 13.5)/(b - (34 - b))
137.5 × (2b - 34) = 311 - 2b
275b - 4675 = 311 - 2b
277b = 4986
b = 18

a = 34 - 18 => a = 16
p = 8.75 × 16 => p = 140
q = 6.75 × 18 + 13.5 => q = 135

Train C is 4 meters longer than train A. Then,
r = p + 4 = 140 + 4 => r = 144

Now, from (ii), we get
6 = r/c
6 = 144/c => c = 24

Train C crosses a platform in 10.5 seconds while train D takes 9 seconds to cross the half of length of the platform crossed by C.

10.5 = (length of platform + r)/c
10.5 = (length of platform + 144)/24
Length of platform = 108

Now, 9 = (length of platform/2 + s)/d
9 = (108/2 + s)/d
s = 9d - 54 …(vii)

Train D crosses a 60 meters long bridge in 3.2 seconds less time taken by train A to cross the same bridge. Then, time taken by train A to cross a 60 meters long bridge
= (p + 60)/a
= (140 + 60)/16
= 12.5 seconds

And time taken by train D to cross 60 meters long bridge = 12.5 - 3.2 = (60 + s)/d
= 9.3d - 60 …(viii)

From (vii) and (viii), we get
9d - 54 = 9.3d + 60
6 = 0.3d
d = 20

And s = 9 × 20 - 54 => s = 126

In tabular form:

Train | Speed in m/s | Length in meters
A | 16 | 140
B | 18 | 135
C | 24 | 144
D | 20 | 126

Length of train E = (135 + 144 + 126)/3 = 135 meters
Speed of train E = (135 + 121)/16 = 16 m/s
Speed of train A = 16 m/s
Therefore, ratio = 16 : 16 = 1 : 1

17. A’ and ‘B’ started walking towards each other at the same time from point ‘X’ and point ‘Y’, respectively. ‘A’ is walking at 6 m/s and ‘B’ is walking at 8 m/s. If distance between ‘X’ and ‘Y’ is 24 metres and they’re travelling back and forth between ‘X’ and ‘Y’, then find the total distance covered by ‘B’ by the time he meets ‘A’ for the second time.

Correct Answer: (c) (288/7) metres 
Solution:

Distance covered by ‘B’ by the time ‘A’ reaches ‘Y’
= 24 + 6 × 8 = 32 metres
Additional distance covered by ‘B’ = 32 - 24
= 8 metres

Distance between ‘A’ and ‘B’ when ‘A’ starts walking back towards ‘X’ = 24 - 8 = 16 metres

Time taken by ‘A’ and ‘B’ to cover 16 metres
= 16 ÷ (6 + 8) = (8/7) seconds

Distance covered by ‘B’ in (8/7) metres = (8/7) × 8
= (64/7) metres

So, total distance covered by ‘B’ = 32 + (64/7)
= (288/7) metres

Hence, option c.

18. The speed of a lion is 90 km/h. When a cheetah and the lion run towards each other along the same path then they meet each other after 5 seconds given that the distance between them initially was 305 metres and they started running at same time. A deer is 140 metres ahead of the cheetah and is running away at the speed of 28 m/s. In how many seconds will the cheetah catch the deer?

Correct Answer: (c) 17.5 seconds 
Solution:

Speed of the lion = 90 ÷ 3.6 = 25 m/s
Relative speed of the lion with respect to the cheetah (when running towards each other) = (305/5) = 61 m/s

So, speed of the cheetah = 61 - 25 = 36 m/s

Relative speed of the cheetah with respect to the deer (running in the same direction) = 36 - 28 = 8 m/s

So, time taken by the cheetah to catch the deer
= (140/8) = 17.5 seconds

Hence, option c.

19. Point ‘A’, ‘B’ and ‘C’ are collinear such that and AB = BC. ‘X’ and ‘Y’ start from point ‘A’ and ‘B’, respectively. If they start at the same time and the distance between them after 2 hours was 120 km and they both meet at point ‘C’, then find the speed of ‘X’.

Correct Answer: (d) 120 km/h 
Solution:

Time taken by ‘X’ and ‘Y’ to cover 120 km = 2 hours
So, relative speed of ‘X’ w.r.t ‘Y’ = 120 ÷ 2 = 60 km/h

So, speed of ‘X’ - speed of ‘Y’ = 60 km/h …(i)

Let distance between point ‘A’ and ‘B’ = ‘a’ km
= distance between point ‘B’ and ‘C’

So, time taken by ‘X’ to cover ‘2a’ km = Time taken by ‘Y’ to cover ‘a’ km

{2a/(speed of ‘X’)} = {a/(speed of ‘Y’)}

speed of ‘X’ = 2 × speed of ‘Y’

So, speed of ‘Y’ = 60 km/h [from (i)]

So, speed of ‘X’ = 60 + 60 = 120 km/h

Hence, option d.

20. Two submarines ‘A’ and ‘B’ are travelling towards each other at 9 km/h and 2 m/s, respectively. If the length of submarine ‘A’ is 200 metres and they take 80 seconds to cross each other, then find the length of submarine ‘B’.

Correct Answer: (e) 160 metres
Solution:

Since, the submarines are travelling towards each other the speed of stream is not relevant because one is travelling in downstream and other is travelling in upstream therefore, speed of stream will cancel out.

Let the length of submarine ‘B’ be ‘x’ metres.
Speed of submarine ‘A’ = 9 × (5/18) = 2.5 m/s

Relative speed of the given submarines = 2.5 + 2 = 4.5 m/sec (Since, they are travelling in opposite direction)

ATQ:
{(200 + x)/4.5} = 80

200 + x = 360
x = 160

So, length of submarine ‘B’ = 160 metres

Hence, option e.