বিসিএস, ব্যাংক, প্রাথমিক শিক্ষক ও সকল সরকারি চাকরির বিগত সালের প্রশ্ন ও অধ্যায়ভিত্তিক নির্ভুল সমাধান
Solution:
Let the actual distance travelled be x km.
Then,
x/12 = (x + 24)/18
⇒ 18x = 12x + 288
⇒ 6x = 288
∴ x = 48 km
Solution:
Length of the train = 350 m
Length of the bridge = 450 m
∴ Total length = (450 + 350) m
= 800m
∴ Speed of the train = 800/40 m/sec
= 20 m/sec
Now total length of the train and new bridge
= (550 + 350) m
= 900 m
∴ Time taken = (900/20) sec = 45 sec
Solution:
Given,
Mr. Sohel can do the job in 8 days
∴ in 1 day Mr. Sohel can do = 1/8 part
and,
His son can do the job in 24 days
∴ in 1 day his son can do = 1/24 part
∴ in 1 day they worked together = (1/8 + 1/24) part
= (3 + 1)/24 part
= 4/24 part
= 1/6 part
Hence, worked together 1/6 part can do in 1 day
∴ They can complete the job in 6 days if they work together
Solution:
Let,
the velocity of the boat be x mph
and the stream be y mph
In upstream,
In 90 minutes he goes 3 miles
In 60 minutes he goes (3 × 60) / 90 = 2 miles
ATQ,
x - y = 2
⇒ x - 2 = 2 [stream's velocity = 2 mph]
⇒ x = 4
So, velocity in downstream = x + y = 2 + 4 = 6 mph
He goes 6 miles in 1 h
He goes 3 miles in = 3/6 = (1/2 × 60) minutes = 30 minutes
Solution:
Downstream speed = 32/4 = 8 km/h
Upstream speed = 32/16 = 2 km/h
∴ Speed of the stream = (8 - 2)/2 = 3 km/h
Solution:
Given that,
A man covers half of his journey at 6 km/h
And The remaining half at 3 km/h.
We know that,
Average speed = 2xy/(x + y)
= (2 × 6 × 3)/(6 + 3)
= 36/9 = 4 kmph
Solution:
Speed in still water = 12 km/h
Speed of the stream = x km/h
Let the distance travelled is = D km
Time taken upstream = 2 × (Time taken downstream)
D/(12-x) = 2 × {D/(12+x)}
⇒ 1/(12-x) = 2/(12+x)
⇒ 12 + x = 24 - 2x
⇒ 3x = 12
∴ x = 4
So, Speed of the stream = 4 km/h
Solution:
Train 1 length = 100 meters
Train 2 length = 100 meters
Total distance = (100 + 100) = 200 meters
Speed of Train 1 = 72 km/h = 72 × (5/18) m/s = 20 m/s
Speed of Train 2 = 54 km/h = 54 × (5/18) m/s = 15 m/s
Relative speed = (20 + 15) = 35 m/s
Time = (200/35) = 5.71 seconds = 5.7 seconds
Solution:
Train length = 240 meters
Time to pass a pole = 15 seconds
Speed = (240/15) m/s = 16 m/s
Total distance to be covered (train + platform) = 240 + 300
= 540 meters
So, Time = 540/16 = 33.75 seconds
Solution:
Speed of the swimmer in still water = 4 km/h
Speed of the current = 2 km/h
Distance one way = 12 km
Downstream Speed = 4 + 2 = 6 km/h
Upstream Speed = 4 - 2 = 2 km/h
Time taken downstream = 12/6 = 2 hours
Time taken upstream = 12/2 = 6 hours
Total time = 6 + 2 = 8 hours
