ব্যাংক ডেইলি কুইজ [লং কোর্সের অংশ]

Question: A person crosses an 800m long street in 5 minutes. What is his speed in km per hour?

Solution: 
distance = 800m = 0.8km
time = 5 minutes = 5/60 = 1/12 hour

speed = distance/time
= 0.8/(1/12) km per hour
= 9.6 km per hour.

Question: Two, trains, one from Sylhet to Dhaka and the other from Dhaka to Sylhet, start simultaneously. After they meet, the trains reach their destinations after 16 hours and 25 hours respectively. The ratio of their speeds is-

Solution: 

let, they meet at X, and Train A and B have the speed of p and y respectively.

in the time of t,
A covers = pt distance
B covers = qt distance

after meeting at X point,
A covers the rest part in 16 hours and B in 25 hours.
so, 
distance covered by A is = 16p
distance covered by B is = 25q

∴ pt = 25q......(i)
and, qt = 16p.......(ii)

from equations (i) and (ii) we we get,
p/q = 25q/16p
p²/q² = 25/16
p/q = 5/4
p : q = 5 : 4

Question: A boy traveled from Dhaka to Comilla at 20kmph and from Comilla to Dhaka at 30kmph. What is his average speed?

Solution: 
Let,
Distance from Dhaka to Comilla = P
From Dhaka to Comilla,
speed = 20kmph
∴ time = P/20 hour

From Comilla to Dhaka,
speed = 30kmph
∴ time = P/30 hour

Average speed = total distance/total time
= 2P/(P/20 + P/30)
= 24 kmph

Question: Nibir, while going to school, passes 200m in 2 minutes, waits for his friend for 5 minutes, and then crosses the next 600m in 4kmph. What is his average speed?

Solution: 
600m or, 0.6km was crossed with 4kmph
time = 0.6/4 h = (0.6/4)60 minutes = 9 minutes

total time = (9 + 2 + 5) minutes = 16 minutes

average speed = total distance/total time
= 800m/16 minutes
= 0.8/(16/60) kmph
= 3 kmph

Question: The ratio between the speeds of two trains is 5 : 8. If the second train runs 600 km in 5 hours, then the speed of the first train is -

Solution:
Let the speed of the trains are 5x and 8x

the speed of the second train = 600/5 kmph = 120 kmph

∴ 8x = 120
x = 15

∴ speed of first train = 5x = 75 kmph

Question: Pavel and Rajib started from the opposite direction of a 10km racing track. Their speed is 15kmph and 10kmph respectively. After which time they will meet if they start simultaneously?

Solution:

let, they will meet after t hour at point X.
in t hour,
A will cross = (15 × t) = 15t km
B will cross = (10 × t) = 10t km

ATQ,
15t + 10t = 10
25t = 10
t = 0.4 hours
= 24 minutes

Question: A takes 30 minutes more than B to reach a destination. The speeds of A and B are in the ratio 4 : 6. Time in which A reaches the destination?

Solution: 
here, ratio of speed is 4 : 6
as the ratio of time is inversly proportional to speed,
ratio of time = 6 : 4

ATQ,
6x - 4x = 30 min
2x = 30 min
x = 15 min = 1/4 hour

A takes total time of = 6 × 1/4 = 1.5 hr

লাইভ পরীক্ষার প্রশ্নে একক m/s এর পরিবর্তে mph দেয়া ছিল। 
প্রশ্নে ভাষাগত ত্রুটি থাকায় প্রশ্নটি বাতিল করা হলো। 
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Question: A mouse started to run at a speed of 10m/s seeing a cat 200m away. The cat noticed the mouse and started to run at a speed of 12m/s at the same time and same direction. How much time does the cat need to catch the mouse?

Solution: 
let the time is t seconds.
in t seconds,
the mouse covers the distance of = (10 × t) = 10t m
the cat covers = (12 × t) = 12t m

ATQ,
12t = 10t + 200
2t = 200
t = 100 seconds.

Question: A beats B by 100 m and C by 150 m in a kilometer race. In the same race, by how many meters does B beat C in that race?

Solution:
Here,
A : B = 1000 : 900
A : C = 1000 : 850

B/C = B/A / C/A
= (B/A) × (A/C)
= (900/1000) × (1000/850)
= 900/850

in 900m B beats C by 50m
∴ in 1000m B beats C by = (50 × 1000)/900 = 50000/900 = 55.55m

Question: A runner crosses a square field diagonally with a side length of 200√2 m in just 20 seconds. How much time will it take to complete the full perimeter of the field?

Solution: 
Diagonal of the square field is = √2 × 200√2 = 400 m

speed = 400 / 20 = 20 mps

perimeter = 4 × 200√2 m

time = 800√2 / 20 = 40√2 seconds

লাইভ পরীক্ষার প্রশ্নে লজিক্যাল ত্রুটি ছিল। 
প্রশ্নে ত্রুটি থাকায় প্রশ্নটি বাতিল করা হলো। 
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Question: A boat in still water travels at a speed of 24 kmph. It goes 40 km downstream in 1 hour 20 minutes. The time taken by it to cover a 45 km distance upstream will be - 

Solution: 
downstream speed = 40/(4/3) kmph
= 30 kmph

speed of stream  = 30 - 24 = 6 kmph

∴ speed upstream = 24 - 6 = 18 kmph

time to cross 45 km is = 45/18 hour
= 2.5 hour
= 2 hour 30 minutes.

Question: A train passes a man at 110 kmph running towards the train at the speed of 10 kmph. If it took 3 seconds to cross the man, what would be the length of the train?

Solution: 
As both of them are facing towards each other.
total speed will be = 110 + 10 kmph
= 120 kmph

length of the train = 120 × (3/3600) km
= 0.1 km
= 100 m

Question: A train passes two bridges of length 800 m and 400 m in 100 seconds and 60 seconds respectively. The length of the train is-

Solution: 
Let the length of the train is x m and speed is s.
ATQ,
s = (x + 800)/100 and,
s = (x + 400)/60

∴ (x + 800)/100 = (x + 400)/60
or, 60x + 48000 = 100x + 40000
or, 40x = 8000
or, x = 200 m

Question: Two runners start running together for a certain distance, one at 5 km/h and another at 8 km/h. The former arrives one and a half an hour before the latter. The distance in Km is -

Solution: 
Let the distance be = P
time of the first runner = P/5 hour
second runner = P/8

ATQ,
P/5 - P/8 = 3/2
3P/40 = 3/2
3P = 60
P = 20 km

Question: In a 200m race, Joy defeats Bishal by 5 seconds. If the speed of Joy is 18 kmph, then the speed of Bishal is- 

Solution: 
speed of Joy = 18 kmph = 18/3.6 = 5 mph
time taken by Joy = 200/5 = 40 sec

time taken by Bishal = 40 + 5
= 45 sec
speed of Bishal = 200/45 mph
= 4.44 mph
= 16 kmph