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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