QUIZ ON RATIO AND PROPORTION

Problem 1 :

The ratio of 8 books to 20 books is

(A) 2 : 5    (B) 5 : 2    (C) 4 : 5    (D) 5 : 4

Solution :

Ratio between 8 books to 20 books = 8 : 20

Dividing both parts by 2, we get

= 4 : 5

So, option C is correct.

Problem 2 :

The ratio of the number of sides of a square to the number of edges of a cube is

(A) 1 : 2        (B) 3 : 2         (C) 4 : 1          (D) 1 : 3

Solution :

Number of sides of a square = 4

Number of edges of cube = 8

Ratio between them,

= 4 : 8

= 1 : 2

So, option A is correct.

Problem 3 :

A picture is 60 cm wide and 1.8 m long. The ratio of its width to its perimeter in lowest form is

(A) 1 : 2     (B) 1 : 3       (C) 1 : 4      (D) 1 : 8

Solution :

Width of the picture = 60 cm

Length of the picture = 1.8 m

100 cm = 1 m

= 1.8 x 100

= 180 cm

Ratio between width and length = 60 : 180

= 1 : 3

So, option B is correct.

Problem 4 :

Neelam’s annual income is $2800. Her annual savings amount to $3600. The ratio of her savings to her expenditure is

(A) 1 : 8    (B) 7 : 9    (C) 1 : 6    (D) 1 : 5

Solution :

Ratio between income to savings.

Income : Savings = 2800 : 3600

= 7 : 9

So, option B is correct.

Problem 5 :

Mathematics textbook for Class VI has 320 pages. The chapter ‘symmetry’ runs from page 261 to page 272. The ratio of the number of pages of this chapter to the total number of pages of the book is

(A) 11 : 320      (B) 3 : 40    (C) 3 : 80     (D) 272 : 320

Solution :

Number of pages of the chapter = 272 - 261

= 11

Ratio between to this chapter : total number of pages

= 11 : 320

So, option A is correct.

Problem 6 :

In a box, the ratio of red marbles to blue marbles is 7:4. Which of the following could be the total number of marbles in the box?

(A) 18       (B) 19       (C) 21         (D) 22

Solution :

Ratio between

blue marbles : red marbles = 7 : 4

Multiplying each part by 1, we get

7(1) : 4(1) ==> 7 : 4

Total number of marbles = 7 + 4 = 11

Multiplying each part by 2, we get

7(2) : 4(2) ==> 14 : 8

Total number of marbles = 14 + 8 = 22

So, option D is correct.

Problem 7 :

On a shelf, books with green cover and that with brown cover are in the ratio 2:3. If there are 18 books with green cover, then the number of books with brown cover is

(A) 12         (B) 24            (C) 27         (D) 36

Solution :

Ratio between green cover : brown cover = 2 : 3

Number of green cover books = 18

Number of green cover books and brown cover books are 2x and 3x respectively.

2x = 18

x = 18/2

x = 9

3x =3 (9)  ==> 27

So, option C is correct.

Problem 8 :

If a bus travels 160 km in 4 hours and a train travels 320km in 5 hours at uniform speeds, then the ratio of the distances travelled by them in one hour is

(A) 1 : 2         (B) 4 : 5          (C) 5 : 8           (D) 8 : 5

Solution :

Time = Distance / Speed

Distance = Time x speed

Distance travelled by bus = 160 x 4 ==> 640

Distance travelled by train = 320 x 5 ==> 1600

Ratio between distance :

= 640 : 1600

= 4 : 5

So, option B is correct.

Problem 9 :

In an election, the votes cast for two of the candidates were in the ratio 5 : 7. If the successful candidate received 20734 votes, how many votes did his opponent receive?

Solution :

Let x be the number of votes received by opponent.

Ratio between Opponent : Successful

5 : 7 = x : 20734

5/7 = x/20734

5(20734) = 7x

Dividing by 7, we get

x = 14180

So, number of votes for opponent is 14180.

Problem 10 :

A metal pipe 3 metre long was found to weigh 7.6kg. What would be the weight of the same kind of 7.8m long pipe?

Solution :

Let x be the weight of 7.8 m long pipe.

length of pipe : weight = 3 : 7.6

3 : 7.6 = 7.8 : x

3/7.6 = 7.8/x

Doing cross multiplication, we get

3x = 7.8(7.6)

Dividing by 3 on both sides, we get

x = 19.76

So, length of 7.8 m pipe is 19.76 kg.