Maths Question (Rate and Ratio)

1. A ship travels 75km in 1.5 hours. Find the distance (in km) that the ship travels



a) in 30 mins if its speed is increased by 2km/h,

initial speed =75/1.5 = 50km/h

distance = (50 + 2) x 0.5 = 26km



b) in 5/4 hours if its speed is reduced by 3m/s.

distance = (50 - 3) x 5/4 = 58.75km





2. On a map, islands A and B are 8 cm apart. A ship sails straight from island A to island B at a speed 45km/h. If the R.F. on the map is 1:1000000, how long (in h) does the journey take?

Actual distance = 8cm x 1000000 = 80km

time taken = 80/45 = 1.77778 hours


3. In a bag, there are altogether 70 red marbeles, blue marbeles and green marbeles. The no. of red marbeles and the no. of blue marbeles are in the ratio of 5:4. The no. of blue marbeles and the no. of green marbeles are in the ratio of 3:2



a) Find respectively the no. of red marbeles, blue marbeles and green marbeles.

red:blue = 5:4 = 15:12

blue:green = 3:2 = 12:8

red:blue:green = 15:12:8

no. of red = 70 x 15/35 = 30

no. of blue = 70 x 12/35 = 24

no. of green = 70 x 8/35 = 16


b) Now, 16 marbeles, in which the ratio of the no. of red marbeles to the no. of blue marbeles to the no. of green marbeles is 4:3:1, are taken away. In the remaining marbeles, find the ratio of the no. of red marbeles : the ratio of the no. of blue marbeles : the ratio of the no. of green marbeles

in the 16 marbeles:

no. of red = 16 x 4/8 = 8

no. of blue = 16 x 3/8 = 6

no. of green = 16 x 1/8 = 2

remaining in the bag:

red:blue:green = (30-8):(24-6):(16-2) = 22:18:14 = 11:9:7

1. A ship travels 75km in 1.5 hours. Find the distance (in km) that the ship travels


a) in 30 mins if its speed is increased by 2km/h,
initial speed =75/1.5 = 50km/h
distance = (50 + 2) x 0.5 = 26km


b) in 5/4 hours if its speed is reduced by 3m/s.
distance = (50 - 3) x 5/4 = 58.75km




2. On a map, islands A and B are 8 cm apart. A ship sails straight from island A to island B at a speed 45km/h. If the R.F. on the map is 1:1000000, how long (in h) does the journey take?
Actual distance = 8cm x 1000000 = 80km
time taken = 80/45 = 1.77778 hours

3. In a bag, there are altogether 70 red marbeles, blue marbeles and green marbeles. The no. of red marbeles and the no. of blue marbeles are in the ratio of 5:4. The no. of blue marbeles and the no. of green marbeles are in the ratio of 3:2


a) Find respectively the no. of red marbeles, blue marbeles and green marbeles.
red:blue = 5:4 = 15:12
blue:green = 3:2 = 12:8
red:blue:green = 15:12:8
no. of red = 70 x 15/35 = 30
no. of blue = 70 x 12/35 = 24
no. of green = 70 x 8/35 = 16

b) Now, 16 marbeles, in which the ratio of the no. of red marbeles to the no. of blue marbeles to the no. of green marbeles is 4:3:1, are taken away. In the remaining marbeles, find the ratio of the no. of red marbeles : the ratio of the no. of blue marbeles : the ratio of the no. of green marbeles
in the 16 marbeles:
no. of red = 16 x 4/8 = 8
no. of blue = 16 x 3/8 = 6
no. of green = 16 x 1/8 = 2
remaining in the bag:
red:blue:green = (30-8):(24-6):(16-2) = 22:18:14 = 11:9:7