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A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?

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Question: A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?

[A].

120 m

[B].

240 m

[C].

300 m

[D].

None of these

Answer: Option B

Explanation:

Speed = 54 x 5 m/sec = 15 m/sec.
18

Length of the train = (15 x 20)m = 300 m.

Let the length of the platform be x metres.

Then, x + 300 = 15
36

x + 300 = 540

x = 240 m.

A goods train runs at the speed of 72 kmph and crosses a 250 m long platform in 26 seconds. What is the length of the goods train?

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Question:
A goods train runs at the speed of 72 kmph and crosses a 250 m long platform in 26 seconds. What is the length of the goods train?

[A].

230 m

[B].

240 m

[C].

260 m

[D].

270 m

Answer: Option D

Explanation:

Speed = 72 x 5 m/sec = 20 m/sec.
18

Time = 26 sec.

Let the length of the train be x metres.

Then, x + 250 = 20
26

x + 250 = 520

x = 270.

The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is:

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Question: The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is:
[A].

200 m

[B].

225 m

[C].

245 m

[D].

250 m

Answer: Option C

Explanation:

Speed = 45 x 5 m/sec = 25 m/sec.
18 2

Time = 30 sec.

Let the length of bridge be x metres.

Then, 130 + x = 25
30 2

2(130 + x) = 750

x = 245 m.

Video Explanation: https://youtu.be/M_d8WufJWKc

A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?

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Question: A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?
[A].

120 metres

[B].

180 metres

[C].

324 metres

[D].

150 metres

Answer: Option D

Explanation:

Speed = 60 x 5 m/sec = 50 m/sec.
18 3

Length of the train = (Speed x Time).

Length of the train = 50 x 9 m = 150 m.
3

Video Explanation: https://youtu.be/q6Xy5JXNp-k

A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?

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Question: A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?

[A].

40 sec

[B].

42 sec

[C].

45 sec

[D].

48 sec

Answer: Option A

Explanation:

Formula for converting from km/hr to m/s:  
X km/hr =		 X x 5 m/s.
18
Therefore, Speed = 45 x 5 m/sec = 25 m/sec.
18 2

Total distance to be covered = (360 + 140) m = 500 m.

Formula for finding Time = Distance
Speed
Required time = 500 x 2 sec = 40 sec.
25

The sum of the squares of three numbers is 138, while the sum of their products taken two at a time is 131. Their sum is:

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Question: The sum of the squares of three numbers is 138, while the sum of their products taken two at a time is 131. Their sum is:
[A].

20

[B].

30

[C].

40

[D].

None of these

Answer: Option A

Explanation:

Let the numbers be a, b and c.

Then, a2 + b2 + c2 = 138 and (ab + bc + ca) = 131.

(a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca) = 138 + 2 x 131 = 400.

(a + b + c) = 400 = 20.

Video Explanation: https://youtu.be/qmJ-0X8j_xQ

A two-digit number is such that the product of the digits is 8. When 18 is added to the number, then the digits are reversed. The number is:

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Question:
A two-digit number is such that the product of the digits is 8. When 18 is added to the number, then the digits are reversed. The number is:

[A].

18

[B].

24

[C].

42

[D].

81

Answer: Option B

Explanation:

Let the ten’s and unit digit be x and 8 respectively.
x
Then, 10x + 8 + 18 = 10 x 8 + x
x x

10×2 + 8 + 18x = 80 + x2

9×2 + 18x – 72 = 0

x2 + 2x – 8 = 0

(x + 4)(x – 2) = 0

x = 2.

A number consists of 3 digits whose sum is 10. The middle digit is equal to the sum of the other two and the number will be increased by 99 if its digits are reversed. The number is:

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Question:
A number consists of 3 digits whose sum is 10. The middle digit is equal to the sum of the other two and the number will be increased by 99 if its digits are reversed. The number is:

[A].

145

[B].

253

[C].

370

[D].

352

Answer: Option B

Explanation:

Let the middle digit be x.

Then, 2x = 10 or x = 5. So, the number is either 253 or 352.

Since the number increases on reversing the digits, so the hundred’s digits is smaller than the unit’s digit.

Hence, required number = 253.

The difference between a two-digit number and the number obtained by interchanging the digits is 36. What is the difference between the sum and the difference of the digits of the number if the ratio between the digits of the number is 1 : 2 ?

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Question:
The difference between a two-digit number and the number obtained by interchanging the digits is 36. What is the difference between the sum and the difference of the digits of the number if the ratio between the digits of the number is 1 : 2 ?

[A].

4

[B].

8

[C].

16

[D].

None of these

Answer: Option B

Explanation:

Since the number is greater than the number obtained on reversing the digits, so the ten’s digit is greater than the unit’s digit.

Let ten’s and unit’s digits be 2x and x respectively.

Then, (10 x 2x + x) – (10x + 2x) = 36

9x = 36

x = 4.

Required difference = (2x + x) – (2x – x) = 2x = 8.

The difference between a two-digit number and the number obtained by interchanging the positions of its digits is 36. What is the difference between the two digits of that number?

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Question: The difference between a two-digit number and the number obtained by interchanging the positions of its digits is 36. What is the difference between the two digits of that number?
[A].

3

[B].

4

[C].

9

[D].

Cannot be determined

Answer: Option B

Explanation:

Let the ten’s digit be x and unit’s digit be y.

Then, (10x + y) – (10y + x) = 36

9(x – y) = 36

x – y = 4.

Video Explanation: https://youtu.be/7QOJjAmGVx0