বিগত সালের প্রশ্ন ও প্রশ্ন ব্যাংক
বিসিএস, ব্যাংক, প্রাথমিক শিক্ষক ও সকল সরকারি চাকরির বিগত সালের প্রশ্ন ও অধ্যায়ভিত্তিক নির্ভুল সমাধান
The man needs time = 50/10 = 5 hours
= (5 × 60)
= 300 minutes
He will also rest 4 times after 10, 20, 30 and 40 miles
Total resting time = 4 × 6 = 24 minutes.
Total time = 300 + 24 = 324 minutes
✅ Final Answer: 324 minutes
Solution:
Speed of the train =(63 - 3)km/hr
= 60km/hr
= (60 × 1000)/3600 m/sec
= 50/3
Time taken to pass the man = 500/(50/3) sec
= 500 × (3/50) sec
= 30 sec
Solution:
Speed of train relative to man = (60 - 6)km/hr
= 54km/hr
= (54 × 1000)/3600 m/sec
= (54 × 10)/36 m/sec
= 15 m/sec
∴ Time taken to pass the man = (120 ÷ 15) sec = 8 sec
Suppose B takes t hours to walk d km.
Then, A takes (t + 2) hours to walk d km.
With double speed, A will take = 1/2(t+2) hours.
∴ t − 1/2(t+2) = 1
⇒ {2t − (t+2)}/2 = 1
⇒ 2t − (t+2) = 2
⇒ t = 4
∴ B takes 4 hours to walk d km.
Let,
Speed of boat = x and, Speed of stream = y
ATQ,
x - y = 24/6 = 4 ...... (i)
x + y = 24/4 = 6 ....... (ii)
From, (ii) – (i),
x + y - x + y = 6 - 4
Or, 2y = 2
∴ y = 1
So, Speed of the stream = 1 km/hr
Let the required speed be x mph
ATQ,
300/60 + 200/x = 7
Or, 200/x = 7 - 5
Or, 200/x = 2
So, x = 100
Let Speed of the man is x kmph.
Distance covered in 10 minutes at 20 kmph = distance
covered in 8 minutes at (20 + x) kmph.
Or, 20×(10/60) = 8/(60(20 + x))
Or, 200 = 160 + 8x
Or, 8x = 40
Hence, x = 5kmph.
Let the speed of the stream be x km/hr.
Then,
Speed downstream = (15 + x) km/hr,
Speed upstream = (15 - x) km/hr
ATQ,
30/(15 + x) + 30/(15 - x) = 4(1/2)
Or, 900/(225 - ) = 9/2
Or, 9 = 225
Or, = 25
∴ X = 5 km/hr
Given:
- Length of train = 125 meters
- Man's speed = 5 km/h
- Time to pass the man = 10 seconds
- Both moving in the same direction
Step 1: Convert man's speed to m/s:
5 km/h = (5 × 1000) / (60 × 60) = 1.39 m/s
Step 2: Use the relative speed formula:
Distance / Time = Relative Speed
125 / 10 = 12.5 m/s (relative speed)
Step 3: Add the man's speed to get train's speed:
Train speed = 12.5 + 1.39 = 13.89 m/s
Step 4: Convert train's speed to km/h:
13.89 × 18/5 = 50 km/h