# Free Ratio and Proportion 01 Practice Test - 6th grade

The method by which two similar quantities are compared by using division is known as comparison by

A.

Ratio

B.

Inverse

C.

Proportion

D.

Reciprocal

#### SOLUTION

Solution : A

A ratio is a method by which two similar quantities are compared by using division.

For comparison by ratio, the quantities must have the same _______.

A.

unit

B.

factors

C.

percentage

D.

value

#### SOLUTION

Solution : A

Two or more quantities can be compared only when they have same unit. If they are not, they must be converted into the same units.

Example: Weight in gram cannot be compared to length in metre and weight in grams and kilograms can be compared only when kilograms is converted into grams or grams into kilograms so that both will be in same unit.

The length of a snake is 10 cm and that of a crocodile is 2 m. Pick the correct statement.

A.

The ratio of length of snake to crocodile is 5 : 1

B.

The ratio of length of snake to crocodile is 1 : 20

C.

Crocodile is 10 times longer than the snake.

D.

Crocodile is 15 times longer than the snake.

#### SOLUTION

Solution : B

Ratio is a method of comparing two quantities having the same unit,

2 m = 200 cm

Hence, the ratio of the length of the snake to crocodile would be
10200=120=1:20

In a school, there were six holidays in the month of April.  Find the ratio of number of holidays to the total number of days in the month of April.

A.

5:1

B.

1:5

C.

30:6

D.

6:30

#### SOLUTION

Solution : B and D

There are 30 days in the month of April. So, the ratio of holidays to the number of days in April would be
630=15=1:5

Which of the following is equivalent to
3 : 2?

A.

8 : 4

B.

9 : 16

C.

12 : 8

D. 8 : 12

#### SOLUTION

Solution : C

A ratio obtained by multiplying or dividing the numerator and the denominator of a given ratio by the same number is called an equivalent ratio.

Hence, when the numerator and the denominator of the given ratio 3 : 2 are multiplied by 4, we get

3×42×4 = 128 =12:8

3 : 2 and 12 : 8 are equivalent ratios.

Partnership is inversely proportional to the amount invested.

A.

True

B.

False

#### SOLUTION

Solution : B

Partnership is directly proportional to the amount invested. As amount invested increases patnership(profit) increases. Hence they are directly proportional.

Which of the following ratios are in proportion?

A.

2:3 :: 4:9

B.

3:5 :: 12:20

C.

1:2 :: 3:6

D.

1:2 :: 4:5

#### SOLUTION

Solution : B and C

Two ratios are said to be in proportion if they are equivalent or equal.
Consider 3:5 :: 12:20
12:20 = 1220 = 35 = 3:5
Hence, they are in proportion

Consider 1:2::3:6
3:6 = 36 = 12 = 1:2
Hence, they are in proportion.
Note that 2: 3 and 4: 9 are not in proportion as the product of extremes (2 × 9 = 18) is not equal to product of means (3  × 4 = 12).

Similarly, 1:2 and 4:5 are not in proportion as the product of extremes (1 × 5 = 5) is not equal to product of means (2  × 4 = 8).

Which of the following options are correct?

A.

4 kg : 20 kg :: 50 : 250

B.

2 dozens : 3 dozens :: 40 : 80

C.

8 liters : 15 liters :: 25: 50

D.

2 km : 3 km :: 1m : 2m

#### SOLUTION

Solution : A

Ratios are in proportion if they are equal or equivalent. This can be verified by using the product of means and product of extremes.

In a: b :: c: d; 'b' and 'c' are means and 'a' and 'd' are extremes.

For 4 kg : 20 kg :: 50 : 250

Product of means = 20 × 50 = 1000
Product of extremes = 4 × 250 = 1000

So, this is in proportion.

For 2 dozens : 3 dozens ::  40 : 80

Product of means = 3 × 40 = 120
Product of extremes = 2 × 80 = 160

So, this is not in proportion.

For  8 liters : 15 liters :: 25 : 50
Product of means = 15 × 25 = 375
Product of extremes = 8 × 50 = 400

So, this is also not in in proportion.

For  2 km : 3 km :: 1 m : 2m
Product of means = 3 × 1 = 3
Product of extremes = 2 × 2 = 4

So, this is also not in in proportion.

The weight of 80 identical books is 400 kg. What is the weight of one such book?

A.

10 kg

B.

5 kg

C.

15 kg

D.

20 kg

#### SOLUTION

Solution : B

Weight of 80 identical books = 400 kg
Weight of 1 such book

=40080=10×4010×8=408=5 kg

Find the value obtained by decreasing 1551 in the ratio 11 : 7.

A. 687
B. 987
C. 787
D. 887

#### SOLUTION

Solution : B

To decrease a quantity in the given ratio a : b, we multiply the given
quantity by  ba
where b < a.

Hence, new quantity
= 1551×711
= 141×7
= 987