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31. Two boats A and B start towards each other from two places, 108 km apart. Speed of the boats A and B in still water are 12 km/h and 15 km/h respectively. If A proceeds down and B up the stream, they will meet after:

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Solution:
Let the speed of the stream be x kmph and both the boats meet after t hour.
According to the question,
(12 + x) × t + (15 - x) × t = 108
Or, 12t + 15t = 108
Or, 27t = 108
∴ t = 10827 = 4 hours
32. The speed of a motor-boat is that of the current of water as 36:5. The boat goes along with the current in 5 hours 10 minutes. It will come back in:

Discuss
Solution:
Let the speed of the motor boat = 36x kmph and speed of current = 5x kmph.
The boat goes along with the current in 5 hours 10 minutes = 316 hour
Hence, Distance=316×(36x+5x)=41x+316kmSpeed of boat upstream=36x+5x=31xkmphHence, time taken to come back=41x×31631x=416hours=6hours50minutes
33. In a 100m race, Kamal defeats Bimal by 5 seconds. If the speed of Kamal is 18 kmph, then the speed of Bimal is:

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Solution:
Time taken by Kamal=10018×518=20secondsHence, Time taken by Bimal20+5=25secondsSo, Bimal's speed=10025=4 =4×185=14.4kmph
34. In a race of 200 meters, B can gives a start of 10 meters to A, and C can gives a start of 20 meters to B. The starts that C can gives to A, in the same race is:

Discuss
Solution:
According to question,
When B runs 200 m meters, A runs 190 meters;
Hence, when B runs 180 meters,
A runs =190×180200   = 171 meters;
When C runs 200m, B runs 180 meters.
Hence,
C will give a start to A by = 200 - 171
= 29 meters
35. In a 1-kilometre race, A can beat B by 30 meters, while in a 500-meter race B can beat C by 25 meters. By how many meters will A beats C in a 100-meter race?

Discuss
Solution:
When A runs 100 meters, B runs 970 meters.
Hence, when A runs 100 meter, b runs 97 meter.
When B runs 500 meter, C runs 475 meter.
When B runs 97 meter, C runs, 475×97500   = 92.15 meter.
Hence,
A will beat C by (100 - 92.15) = 7.85 meters.
36. A plane left half an hour later than the scheduled time and in order to reach its destination 1500 kilometers away in time, it had to increase its speed by 33.33 percent over its usual speed. Find its increased speed.

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Solution:
By increasing the speed by 33.33%, it would be able to reduce the time taken for traveling by 25%.
But since this is able to overcome the time delay of 30 minutes, 30 minutes must be equivalent to 25% of the time originally taken.
Hence, the original time must have been 2 hours and the original speed would be 750 kmph.
Hence, the new speed would be 1000 kmph.
37. A car driver, driving in a fog, passes a pedestrian who was walking at the rate of 2 km/h in the same direction. The pedestrian could see the car for 6 minutes and it was visible to him up to distance of 0.6 km. what was speed of the car?

Discuss
Solution:
In 6 minutes, the car goes ahead by 0.6 km.
Hence, the relative speed of the car with respect to the pedestrian is equal to 6 kmph.
Hence, Net speed of the car is 8 kmph.
38. A cyclist moving on a circular track of radius 100 meters completes one revolution in 2 minutes. What is the average speed of cyclist (approx.)?

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Solution:
Distance covered in one complete revolution
=2πr=2×100×227≈628mAveragespeed=6282=314m/min
39. Between 5 am and 5 pm of a particular day for how many times are the minute and the hour hands together?

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Solution:
It will come 11 times together.
40. Two rifles are fired from the same place at a difference of 11 minutes 45 seconds. But a man who is coming towards the place in a train hears the second sound after 11 minutes. Find the speed of train. (speed of sound = 330 m/s)

Discuss
Solution:
Distance travelled by man-train in 11 minute = distance traveled by sound in (11 min 45 sec - 11 min) = 45 sec.
Let the speed of train be x kmph.
Now,
Or, x×1160=453600×330×185
Or, x = 81 kmph.

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