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বিগত নিয়োগ পরীক্ষার প্রশ্নসমুহ ও সমাধান
#1698
✍️ 1. TWO PERSONS ARE RUNNING IN 3.6 KM/H AND 7.2 KM/H SPEED. A TRAIN PASSES THEM IN 9 AND 9.5 SECONDS. WHAT IS THE LENGTH OF THE TRAIN AND SPEED OF THE TRAIN? (PKB SEO - 2018)

(v-3.6) 9 =(v-7.2) 9.5
9V-32.4 =9.5-68.4
V=72 km/hr.
Length of the train = (72-3.6)*5/18*9 = 171 meter

Similar Math for Practice
✍️ 2. A TRAIN PASSES TWO PERSONS WALKING IN THE SAME DIRECTIONS AT A SPEED 5 KM/HR AND 7 KM/HR RESPECTIVELY IN 10 SEC AND 11 SEC RESPECTIVELY. FIND THE SPEED OF THE TRAIN?

(v-5) 10 =(v-7) 11
10V-50 =11v-77.
V=27 km/hr.

✍️ 3. A train overtakes two persons walking along a railway track. The first one walks at 4.5 km/hr. The other one walks at 5.4 km/hr. The train needs 8.4 and 8.5 seconds respectively to overtake them. What is the speed of the train if both the persons are walking in the same direction as the train?
✍️ 4. A train overtakes two persons who are walking in the same direction in which the train is going, at the rate of 2 kmph and 4 kmph and passes them completely in 9 and 10 seconds respectively. The length of the train is:

✍️ 5. A train passed a man standing on a railway platform in 4 seconds and a train coming from the opposite direction passed him in 5 second. If the length of both trains are equal, then how much time will they take to pass each other?

Let, The length of each train be 20 (LCM of 4 & 5)
Now, Speed of 1st train =20/4=5 meters
And, Speed of 2nd train=20/5=4 meters.
Relative speed=5+4=9 meters
Relative length of Two train=20+20=40 meters
So, Required time=40/9
=4 (4/9) (Ans.)

✍️ 6. A man standing on a platform finds that a train takes 3 seconds to pass him and another train of the same length moving in the opposite direction, takes 4 seconds. The time taken by the trains to pass each other will be (Basic Bank AM-2018)
Let, The length of each train be 12 (LCM of 3 & 4)
Now, Speed of 1st train =12/3=4 meters
And, Speed of 2nd train=12/4=3 meters.
Relative speed=4+3=7 meters
Relative length of Two train=12+12=24 meters
So, Required time=24/7
=3 (3/7) (Ans.)

✍️ 7. A train 300 m long, overtake a man walking along the line (in the same direction of the train) at the speed of 4 kms per hour and passed him in 30 sec. The train reached the station in 15 minutes after it has passed the man. In what time did the man reach the station? (Combined 3 Bank Senior Officer-2018)
Relative speed of train & man
= 300/30 = 10m/s = 10 x 18/5 = 36kmph
Speed of man = 4kmph
=> Speed of Train = 36 + 4 = 40kmph
Train travels 15/60 x 40 = 10km after crossing man.
Man will reach station after 10/4 = 2.50 hours.

✍️ 8. A train 400 m long overtake a man walking along the line in the same direction as the train, at the rate of 5 kmph and passed him in 40 seconds. The train reached the station in 20 minutes after passing the man. In what time did the man reach the station?

Relative speed of train & man
= 400/40 = 10m/s = 10 x 18/5 = 36kmph
Speed of man = 5kmph
=> Speed of Train = 36 + 5 = 41kmph
Train travels 20/60 x 41 = 41/3 km after crossing man.
Man will reach station after 41/3*5 = 41/15 hours.

এই ম্যাথ এর সমাধান কোন কোন সাইটে ২.৪৮, ২.৪৪ । আগারওয়ালে ২ ঘণ্টা ৪৮ মিনিট ৪৮ সে। সঠিক টা কারো জানা থাকলে জানাবেন।

✍️ 9. The distance between two stations 'X and Y' is 450 km. A train L Starts at 6:00 pm from X and moves towards Y at an average speed of 60 km/h. Another train M starts from Y at 5 : 20 pm and moves towards X at an average speed of 80 km/h. How far from x will the two trains meet and at what time? (Sonali Bank FF Office-2019)

As Train M starts at 5.20 PM, so in 40 minutes Train M covers,
60 min =40 km
40 min =80*40/60 =53.33 km
So, Remaining Distance = (450-53.33 )= 396.67 km
As L starts from opposite direction,
Total speed =80+60 =140 km/hr.
140 km =60 minutes
396.67 km =60*396.67/140 =170 minutes
So, both train meet at 8.50 PM
Distance covered from X
60 min =60 km
170 min =60*170/60 =170 km (Ans.)

✍️ 10. Two trains are traveling in opposite direction at uniform speed 75 and 60 km/hr respectively. They take 8 seconds to cross each other. If the two had traveled in the same direction, then a passenger sitting in the faster moving train would have overtaken the other train in 31(1/2) sec. The length of the trains in meters are? (Combined 8 bank SO-2019, Sonali Bank Officer-2018)

Relative Speed in opposite Direction = (75+60) * 5/18 = 37.5 m/s
In 8 seconds they covered distance = 37.5*8 = 300 meter
Relative Speed in Similar Direction = (75-60) * 5/18 = 75/18 m/s
In 63/2 seconds they covered distance = 75/18*63/2 = 131.25 meter
The length of another train = (300=131.25) = 168.75 meter

✍️ 11. A cow was standing on a bridge, 5m away from the middle of the bridge. a train was coming towards the bridge from the ends nearest to the cow.seeing this cow ran towards the train and managed to escape when the train was 2m away from the bridge.if it had run in the opposite direction.it would hit by the train 2m before the end of the bridge.what is the length of the bridge in meters.assuming the speed of the train is 4times that of cow. (Combined Oficer-2019)

(This Solution is Collected from Magic of Math)

Let, Length of the Bridge 2B
Then, Cover distance opposite the train by Cow is (B-5) m
Covered distance in same direction to train by cow is (B+5-2) m = (B+3) meters
Difference of distance = (B+3)-(B-5) = 8 meters
Again, Ratio of Speed of T:C = 4:1
Relative Speed of opposite direction: Same direction is = (4+1): (4-1) = 5:3
Difference between relative speed ratio is = 5-3 = 2
Now, ratio 2 is equivalent to 8 meters
Then ratio (5+3)= 8 is equivalent to 8*8/2 = 32 meters
Answer: 32 meters

✍️ 12. A train travelling at 20m/s completely crosses another train having 192 meters length travelling in same direction at 15 m/s in 1.5 minutes. In what time will they cross each other travelling in opposite direction and length of the faster train is? (combined 2 Bank Officer-2018)

Distance Covered in Similar Direction = (20-15)* 90 = 450 meter
So, Length of the faster train = 450- 192 = 258 meter
They will cross in Opposite Direction = 450/20+15 = 450/35 = 12.86 seconds

কোন ভুল হলে ক্ষমা সুন্দর দৃষ্টিতে দেখবেন এবং ভুলটি ধরিয়ে দিবেন।
Happy Reading :)

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