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ANSWERS
1.(2)
Initial speed of motor = 70 kmph.
Distance covered in first 2 hours= 2 × 70 = 140 kms
For next two hours speed of motor = 80 kmph
∴ Distance covered in next 2 hours = 2 × 80 = 160 kms.
Distance covered in first 4 hours= 140 + 160 = 300
Remaining distance = 345 – 300 = 45 km
This distance will be covered at the speed of 90 kmph.
∴ Time taken = 45/90 = ½ hours
∴ Total time taken
= 4 + ½ = 9/2 hours
2.(5)
Let the length of train be x meters.
Time taken in crossing the pole = x/20
Time taken in crossing the bridge= 4x/20
As given, 4x/20 – x/20 = 24
= 3x/20 = 24
= x = (24 × 20)/3
= 160 m
3.(2)
Time taken in walking one way + riding other way= 6 hours 35 minutes ……….. (i)
Time taken riding both ways
= 4 hours 35 minute ………. (ii)
By equation (i) × 2 – (ii),
2 × Time taken in walking one way
= 13 hours 10 minutes – 4 hours = 35 minutes
= 8 hours 35 minutes
4.(4)
When a train crosses a platform, the distance covered = Length of platform and the train.
Speed = Length of(Platform + train)/Time taken
Thus we have inadequate data.
5.(3)
Let the speed of boat in still water= x kmph
∴ Speed of current = x/2 kmph
When boat runs downstream,
30/(x + x/2) = 2
= (30 × 2)/3x = 2
= 6x = 60
= x = 60/6 = 10 kmph
6.(5)
Let the require distance be x km.
According to the question,
x/40 – x/45 = 1
= (9x – 8x)/360 = 1
= x/360 = 1
= x = 360 km
7.(3)
Length of the train = 240 metre
∴ Length of the platform= 480 metre
We know that when a train crosses a platform, it covers a distance equal to the sum of its length and that of platform.
∴ Speed of train= (240 + 480)/40 m/sec
= 720/40 = 18 m/sec
8.(1)
Distance between Ramgarh and Devgarh = (50 ×44/60) = 110/3
New speed = 55 kmph= 55/60 km/minute
∴ Required Time = Distance/ Speed
= 110/3 × 60/55 = 40 minutes
9.(5)
Required ratio = 6 : 4 = 3 : 2
[As time taken is inversely proportional to the speed.]
10.(1)
Let the distance between villages A and B be xkm.
∴ x/40 – x/60 = 2
= (3x – 2x)/120 = 2
= x = 2 × 120 = 240 km
