PROBLEMS ON RATIO PROPORTION AND UNITARY METHOD

Problem 1 :

The cost of 6 chocolates is $210, then find the cost of 4 chocolates.

Solution :

Cost of 6 chocolates = $210

Using unitary method, let us find the cost of 1 chocolate.

Cost of 1 chocolate = 210/6

= $35

Cost of 4 chocolates = 4 x 35

= 140

So, cost of 4 chocolates is $140.

Problem 2 :

Express the ratio in simplest form.

45 minutes to 4 hours.

Solution :

Two quantities of same kind is called ratio.

4 hours = how many minutes

1 hour = 60 minutes

4 hours = 4 x 60

= 240 minutes

= 45 : 240

= 9 : 48

= 3 : 16

Problem 3 :

Check whether the following ratios are in proportion or not.

8 : 21 and 24 : 63

Solution :

8 : 21 :: 24 : 63

If the given ratios are in proportion, the following property will hold.

Property of means = product of extremes

8 (63) = 21 (24)

504 = 504

Since they are equal, they are in the proportion.

Problem 4 :

Find the value of x if the following are in proportion.

27 : x and 63 : 84

Solution :

27 : x :: 63 :84

Product of means = product of extremes

27 ⋅ 84 = x ⋅ 63

27(x) = 84(63)

x = 84(63)/27

x = 196

Problem 5 :

If the cost of 14 m cloth is $1890. Find the cost of 6 m of cloth.

Solution :

Cost of 14 m cloth = $1890

Cost of 1 m cloth = 1890/14

= $135

Cost of 6 m cloth = 135 (6)

= $810

So, cost of 6 m cloth is $810.

Problem 6 :

Manoj weight is 36 kg. His brother's weight is 2 kg more. Find the ratio of weight of Manoj and his brother.

Solution :

Manoj's weight = 36 kg

His brother's weight = 38 kg

Ratio between Manoj and his brother = 36 : 38

= 18 : 19

Problem 7 :

The ratio of the number of male and female in a textile mill is 5 : 3. If there are 115 male workers, what is the number of female workers in the mill.

Solution :

Number of male workers = 5x

number of female workers = 3x

5x = 115

x = 115/5

x = 23

Number of female workers = 3(23)

= 69 female workers.

Problem 8 :

The value of m, if 3, 18, m, 42 are in proportions is 

a)  6   b)  54   c)  7

Solution :

3 : 18 = m : 42

3/18 = m/42

Doing cross multiplication, we get

3(42) = 18 m

m = 3(42)/18

m = 7

So, the value of m is 7.

Problem 9 :

Are the following numbers in continued proportion.

36, 90, 75

Solution :

Definition :

a proportion in which the consequent of each ratio is the antecedent of the next

That is,

36 : 90 = 90 : 75

Product of extremes = product of means

36 (75) = 90 (90)

2700 ≠ 8100

They are not equal, so they are not in continued proportion.

Problem 10 :

4, x, 9 are in continued proportion, find the value of x.

Solution :

If 4, x, 9 are in continued proportion, then

4 : x :: x : 9

4/x = x/9

36 = x²

x = √36

x = 6

Problem 11 :

If 20% of x = 30% of y, then x : y = ?

Solution :

20% of x = 30% of y

20x/100 = 30y/100

Ignoring the same denominators,

20x = 30y

x/y = 30/20

x : y = 3 : 2

Problem 12 :

Present ages of Rani and Kami are in the ratio of 5 : 6 respectively. 7 year hence this ratio will become 6 : 7 respectively. What is Rani's present age ?

Solution :

Let 5x and 6x be Rani's and Kami's present ages respectively.

7 years after their ages will be 5x + 7 and 6x + 7

(5x + 7)/(6x + 7) = 6/7

7(5x + 7) = 6(6x + 7)

35x + 49 = 36x + 42

35x - 36x = 42 - 49

-1x = -7

x = 7

Rani's present age = 5(7) ==> 35 years