Ratio: Word Problems

Word Problem 1

The difference between the capacities of a jar and a bottle is 300 ml. If the capacities of the bottle and the jar are in the ratio 3 : 5, what is the maximum volume of water in ml that they can hold together?



2 units  =  300 ml
1 unit  =  300 ml ÷ 2
   =  150 ml
8 units  =  150 ml × 8
   =  1200 ml

They can hold 1200 ml of water together.

Word Problem 2

The ratio of the breadth of a rectangle to its perimeter is 1 : 8. Find the area of the rectangle if its length is 45 cm.

Perimeter = 2 × (Length + Breadth)

Length + Breadth = Perimeter ÷ 2

Length = (Perimeter ÷ 2) − Breadth
          = (8 units ÷ 2) − 1 unit
          = 3 units



3 units  =  45 cm
1 unit  =  45 cm ÷ 3
   =  15 cm

The breadth of the rectangle is 15 cm.

Area  =  length × breadth
   =  45 cm × 15 cm
   =  675 cm2

The area of the rectangle is 675 cm2.

Word Problem 3

Sally had $200 at first. She spent a sum of money on a dress, a necklace and a ring in the ratio 7 : 4 : 5. If she spent $108 on the jewellery, how much money had she left?



9 units  =  $108
1 unit  =  $12
16 units  =  $12 × 16
   =  $192
She spent $192 altogether.

$200 − $192  =  $8
 
She had $8 left.

Word Problem 4

The lengths of 3 poles are in the ratio 4 : 5 : 10. The shortest pole is 48 cm shorter than the longest pole. What is the length of the poles altogether?




6 units  =  48 cm
1 unit  =  48 cm ÷ 6
   =  8 cm
19 units  =  8 cm × 19
   =  152 cm

The length of the poles is 152 cm altogether.

Word Problem 5

Pam travelled   1 
11
  of the distance of her journey by car while the rest
by bus and train in the ratio 1 : 4. If she travelled 532 km more by train than by car, how far did she travel?



1 : 4  =  2 : 8

So,
Bus 2 units
Train 8 units
8 units − 1 unit  =  7 units

She travelled 7 units more by train than by car.

7 units  =  532 km
1 unit  =  532 km ÷ 7
   =  76 km
11 units  =  76 km × 11
   =  836 km

She travelled 836 km.

Word Problem 6

A pet parrot shop has 322 parrots that are coloured either green or blue or yellow. The ratio of the number of green parrots to the number of blue parrots is 13 : 4. The ratio of the number of blue parrots to the number of yellow parrots is 2 : 3.

    a)    Find the ratio of the number of green parrots to the number of blue parrots to the number of yellow parrots.
 b)Find the number of green parrots.

     

a)   Number of green parrots : Blue parrots : Yellow parrots
 =  13 : 4 : 6

b)   23 units  =  322
 1 unit  =  322 ÷ 23
    =  14
 13 units  =  14 × 13
    =  182

       There were 182 green parrots.

Word Problem 7

In a school, for every 5 children born in January there were 3 born in February and for every 2 children born in February there were 5 born in March.

    a)    What is the ratio of the number of children born in January to the number of children born in March?
 b)    How many children were born in the three months altogether if 255 of them were born in March?

    

a)   Number of children born in January : Born in February
 =  5 : 3
 =  10 : 6
 
 Number of children born in February : Born in March
 =  2 : 5
 6 : 15
 
 Number of children born in January : Born in March
 =  10 : 15
 =  2 : 3

b)   15 units  =  255
 1 unit  =  255 ÷ 15
    =  17
 31 units  =  17 × 31
    =  527

       There were 527 children born in the three months altogether.

Word Problem 8

Rayan received twice as much pocket money as Falaq. After Rayan spent $5 on animal cards, the ratio of Rayan's amount to that of Falaq's became 3 : 2. Find the amount of pocket money that Falaq received.



1 unit  =  $5
2 units  =  $5 × 2
   =  $10
 
Falaq received $10.

Word Problem 9

The ratio of Grace's mass to Laura's mass was 7 : 5 at first. Then, Laura fell
sick and lost   1 
10
  of her mass. The new difference between their body
masses was 25 kg.

    a)    Find Grace's mass.
 b)    What is the new ratio of Grace's mass to Laura's mass?


a)   5 units  =  25
 1 unit  =  25 ÷ 5
    =  5
 14 units  =  5 × 14
    =  70

       Grace's mass was 70 kg.

b)   Grace's mass : Laura's mass
 =  14 : 9

       The new ratio of Grace's mass to Laura's mass is 14 : 9.

Word Problem 10

Abby and Nina share a sum of money in the ratio 2 : 3. Then, Nina gives a sixth of her share to Abby.

    a)    Do they now have equal amounts of money?
 b)    If Abby now has $125, how much money had she at first?


a)   Abby's amount of money  =  5 units
 Nina's amount of money  =  5 units
 5 : 5   =  1 : 1

       Yes, they now have equal amounts of money.

b)   5 units  =  $125
 1 unit  =  $125 ÷ 5
    =  $25
 4 units  =  $25 × 4
    =  $100
 
 Abby had $100 at first.

Word Problem 11

The ratio of the number of laptops to the number of printers in an electronics store was 2 : 5 at first. After a shipment of 240 new laptops arrived at the store, there were twice as many laptops as printers.

    a) Find the number of printers in the electronics store?
 b)    If a shipment of 120 new printers arrived at the store, what would the ratio of the number of laptops to the number of printers now be?
a)   
 
8 units  =  240
1 unit  =  240 ÷ 8
   =  30
5 units  =  30 × 5
   =  150
 
There were 150 printers.


b)   
 
Number of laptops in the store  =  10 units
   =  30 × 10
   =  300
Number of printers in the store  =  150 + 120
   =  270
Number of laptops : printers  =  300 + 270
   =  10 : 9
 
The new ratio would be 10 : 9.

Word Problem 12

Roy, Danny and Henry had a collection of hats. The ratio of the number of hats that Roy had to the number of hats that Danny had to the number of
hats that Henry had was 4 : 5 : 6. Then, Henry gave  1
4
  of his hats to Roy.

    a)    What is the new ratio of the number of Roy's hats to that of Danny's to that of Henry's?
 b)  If Roy now has 44 hats, how many hats has Danny?



a)   Before
 Number of Roy's hats : Danny's hats : Henry's hats
 =   4 : 5 : 6
 =   8 : 10 : 12
 
      After
 Roy    8 units + 3 units  =  11 units
 Henry    12 units − 3 units  =  9 units

       The new ratio of the number of Roy's hats : Danny's hats :
       Henry's hats is 11 : 10 : 9.

b)   11 units  =  44
 1 unit  =  44 ÷ 11
    =  4
 10 units  =  40
 
 Danny has 40 hats.