ব্যাংক ডেইলি কুইজ [লং কোর্সের অংশ]

Question: A vehicle travels at the rate of 80 kmph. What distance will it travel in 15 minutes?

Solution:
In 60 minutes it goes 80 k.m. = 80000 m
In 1 minute it goes 80000/60 m
In 15 minutes it goes (80000 × 15)/60 k.m.
= 20000 meters.

Question: An old man is walking on a foggy road at a speed of x km/hr. Due to low visibility, the old man see only up to 600 meters. If a car overtakes the man from behind with the speed of 15 km/hr then the man can see the car for 216 seconds. Find the speed of the man?

Solution:
Distance up to old man see = 600/1000 = 0.6 km
Time for which the man can see the car = 216/ (60 × 60) = 0.06 hour

ATQ,
0.6/(15 - x) = 0.06
⇒ 15 - x = 10
⇒ x = 5

Hence, the correct answer is 5 km/hr.

Question: A train 900 meters long is running at a speed 78 kmph. If it crosses a tunnel in 1 min, then the length of the tunnel is-

Solution:
৩৬০০ সেকেন্ডে অতিক্রম করে ৭৮০০০ মি.
১ সেকেন্ডে অতিক্রম করে ৭৮০০০/৩৬০০ মি.
৬০ সেকেন্ডে অতিক্রম করে (৭৮০০০ × ৬০)/৩৬০০ মি.
= ১৩০০ মি.

টানেলের দৈর্ঘ্য = ১৩০০ - ৯০০ = ৪০০ মি.

Question: Two trains travel in opposite directions at 36 km/hr and 45 km/hr and a man sitting in slower train passes the faster train in 8 seconds. The length of the faster train is:

Solution: 
As the trains travel in opposite directions then 
Relative speed = (45 + 36)km/hr.
= 81 km/hr.
= (81 × 1000)/3600
= 45/2


 The length of the faster train = (45/2) × 8
= 180 m 

Question: With an average speed of 50 km/hr, a train reaches its destination in time. If it goes with an average speed of 40 km/hr, it is late by 24 min. The total journey is:

Solution:
Difference between timings = 24 min = 24/60 hr = 2/5 hr.
Let the length of the journey be x km.

Then,
(x/40) - (x/50) = 2/5
Or, (5x - 4x)/200 = 2/5
Or, x/200 = 2/5
Or, x = (25 × 200)
∴ x = 80 km.

∴ The total journey is 80 km.

Question: A person rowing against the current can go 2 km per hour. If the speed of the current is 3 km per hour, how much time will he take to cover 32 km, rowing along the current?

Solution: 
ধরি, ব্যক্তির বেগ x কিমি/ঘণ্টা 
স্রোতের বেগ ৩ কিমি/ঘণ্টা

ব্যক্তি স্রোতের বিপরীতে ২ কিমি/ঘণ্টা বেগে যায়।

x - ৩ = ২
∴ x = ৫ কিমি/ঘণ্টা 

স্রোতের অনুকূলে বেগ = ৩ + ৫ কিমি/ঘণ্টা 
= ৮ কিমি/ঘণ্টা 

স্রোতের অনুকূলে যেতে সময় লাগে = ৩২/৮ ঘণ্টা 
= ৪ ঘন্টা 

Question: A man travels 50 km at speed 25 km/hr and next 40 km at 20 km/hr and there after travel 90 km at 15 km/hr. His average speed is:

Solution:
We know,
Average speed = Total distance/Total time
= (50 + 40 + 90)/(2 + 2 + 6) km/hr
= 180/10 km/hr
= 18 km/hr.

Question: A man can row 6 km/hr in still water. If the speed of the current is 2 km/hr, it takes 3 hrs more in upstream than in the downstream for the same distance. The distance is-

Solution:
Let distance = x
Speed of man in still water, = 6 km/h
Speed of current, = 2 km/h

Now
{x/(6 - 2)} - {x/(6 + 2)} = 3
⇒ (x/4) - (x/8) = 3
⇒ (2x - x)/8 = 3
⇒ x/8 = 3
∴ x = 24 

∴ Distance = 24 km.

Question: A train running at a speed of 90 km/hr crosses a platform double its length in 36 seconds. What is the length of the platform in meters?

Solution:
Let, the length of the train be x metres.
Then, the length of the platform = 2x metres.
Speed of the train = 90 × (1000/3600) m/sec
= 25 m/sec

ATQ,
(x + 2x)/25 = 36
⇒ 3x = 900
⇒ x = 300

Hence, the length of platform = 2x = (2 × 300) m
= 600 m

Question: Saiful traveled 2/3 as km on foot as by water and 1/3 as km on bus as by water. If he covered a total of 48 km, how many km did he travel on foot?

Solution:
Let, he traveled x km by water, 2x/3 km on foot and x/3 km bus

ATQ,
x + (2x/3) + (x/3) = 48
⇒ (3x + 2x + x)/3 = 48
⇒ 6x = 144
⇒ x = 24

So, traveled (2 × 24)/3 = 16 km on foot.