Question: Maruf is travelling on his cycle and he calculated to reach point A at 3 p.m. if he travels at 10 kmph, he will reach there at 1 p.m. if he travels at 15 kmph. At what speed must he travel to reach A at 2 p.m.

Solution: 

Let the distance travelled by x km.

ATQ, 

x/10 - x/15 = 2 

⇒ 3x - 2x = 60 

∴ x = 60

Time taken to travel 60 km at 10km/h = 60/10 hours

= 6 hours

So, Maruf started 6 hours before 3 P.M. i.e., at 9 Α.Μ.

∴ Required speed = 60/5 kmph. 

= 12 kmph.

Question: A man takes twice as long to row a distance against the stream as to row the same distance in favour of the stream. The ratio of the speed of the boat (in still water) and the stream is:

Solution:

Let man's rate upstream be x kmph.

Then, his rate downstream = 2x kmph.

∴ (Speed in still water) : (Speed of stream) = {(2x + x)/2} : {(2x - x)/2}

= (3x/2) : (x/2)

= 3 : 1

Question: The ratio between the speeds of a bus and bike is 5 : 8. If the bus travels 120 km in 2 hours, find the speed of the bike.

Solution: 

Let, 

the speed of bus and bike is 5x and 8x. 

Speed of bus = 120/2 

= 60 km/h 

ATQ,

5x = 60

⇒ x= 60/5 

∴ x = 12

Speed of bike = 8x = (8 × 12) = 96 km/h