31. Sanjay cycles at the speed of 100 m/min. How long will he take to travel 10km?
In 1 min Sanjay cycles 100 m
In 1 hr (i.e. 60 min) he cycles 6000 m = 6 km
So he will take 1 hr 40 min for 10 km.
For 100 m Sanjay takes 1 min
For 10 km (= 10 000 m), he will take 100 min.
i.e. 1 hr 40 min.

32. Murugan drove to the next town and he had planned to reach there by a certain time. When half the time was over, he realised that he had covered only two-fifths of the distance. So he increased his speed and managed to reach in time. He had to increase the speed by
In half the time he covered only 2 out of 5 parts.
In the next half the time (equal time)
he has to cover 3 parts (insead of the 2); half the distance extra;
so half the speed, i.e. 50%, extra.
Increase in speed is 50%.

33. Parvathi drove to her aunt's place at 60 kmph and reached in 8 hours. On return she drove at 80 kmph. How long did she take?
Ratio of speeds is 60 : 80 = 3 : 4
Ratio of times, (inverse of speeds ratio), is 4 : 3
So she reached in 6 hours.

34. Siva walked to his uncle's place at 4 kmph and returned at 6 kmph. If he took 5 hours in all, how far was his uncle's place?
Distance same.
Average Speed, av speed (1K) = av speed 2 (1K) 4.8 kmph
Total distance is 4.8 x 5 = 24 km
Uncle's place is 12 km away.

35. Usually Mani takes 40 min. to the Railway station just in time for his train. Today he started from home 10 minutes late. How much faster should he go to catch the same train?

Available time 30 min.
Ratio of time is 4:3.
So ratio of speed 3:4.
He should be (1 part out of 3 parts),   Fr_1-3 (1K)   faster today.

Result in percentage:

  Fr_1-3 (1K)
of a 100, so 33 Fr_1-3 (1K) %   faster today.