Class 6 Important Questions for Maths - Ratio and Proportion ... - Free Printable

Let's solve each problem step by step:

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Problem 1:

The ratio of 8 books to 20 books is:
(A) 2 : 5
(B) 5 : 2
(C) 4 : 5
(D) 5 : 4

Solution:
To find the ratio of 8 books to 20 books, we simplify the fraction:
\[
\frac{8}{20} = \frac{8 \div 4}{20 \div 4} = \frac{2}{5}
\]
Thus, the ratio is \(2 : 5\).

Answer: (A) 2 : 5

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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:
- A square has 4 sides.
- A cube has 12 edges.
The ratio of the number of sides of a square to the number of edges of a cube is:
\[
\frac{4}{12} = \frac{4 \div 4}{12 \div 4} = \frac{1}{3}
\]
Thus, the ratio is \(1 : 3\).

Answer: (D) 1 : 3

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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 = 180 cm
- Perimeter of the rectangle = \(2 \times (\text{length} + \text{width})\)
\[
\text{Perimeter} = 2 \times (180 + 60) = 2 \times 240 = 480 \text{ cm}
\]
The ratio of the width to the perimeter is:
\[
\frac{\text{Width}}{\text{Perimeter}} = \frac{60}{480} = \frac{60 \div 60}{480 \div 60} = \frac{1}{8}
\]
Thus, the ratio is \(1 : 8\).

Answer: (D) 1 : 8

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Problem 4:

Neelam’s annual income is Rs. 288000. Her annual savings amount to Rs. 36000. The ratio of her savings to her expenditure is:
(A) 1 : 8
(B) 1 : 7
(C) 1 : 6
(D) 1 : 5

Solution:
- Annual income = Rs. 288000
- Annual savings = Rs. 36000
- Expenditure = Income - Savings
\[
\text{Expenditure} = 288000 - 36000 = 252000
\]
The ratio of savings to expenditure is:
\[
\frac{\text{Savings}}{\text{Expenditure}} = \frac{36000}{252000} = \frac{36000 \div 36000}{252000 \div 36000} = \frac{1}{7}
\]
Thus, the ratio is \(1 : 7\).

Answer: (B) 1 : 7

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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:
- Total number of pages in the book = 320
- Pages in the chapter 'symmetry' = 272 - 261 + 1 = 12
The ratio of the number of pages of the chapter to the total number of pages is:
\[
\frac{\text{Pages in symmetry}}{\text{Total pages}} = \frac{12}{320} = \frac{12 \div 4}{320 \div 4} = \frac{3}{80}
\]
Thus, the ratio is \(3 : 80\).

Answer: (C) 3 : 80

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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:
- The ratio of red marbles to blue marbles is 7:4.
- Let the number of red marbles be \(7x\) and the number of blue marbles be \(4x\).
- Total number of marbles = \(7x + 4x = 11x\)
The total number of marbles must be a multiple of 11. Checking the options:
- 18 is not a multiple of 11.
- 19 is not a multiple of 11.
- 21 is not a multiple of 11.
- 22 is a multiple of 11 (\(22 = 11 \times 2\)).

Thus, the total number of marbles could be 22.

Answer: (D) 22

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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:
- The ratio of green books to brown books is 2:3.
- Let the number of green books be \(2x\) and the number of brown books be \(3x\).
- Given that the number of green books is 18:
\[
2x = 18 \implies x = \frac{18}{2} = 9
\]
- Number of brown books = \(3x = 3 \times 9 = 27\).

Thus, the number of books with brown cover is 27.

Answer: (C) 27

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Problem 8:

The greatest ratio among the ratios 2 : 3, 5 : 8, 75 : 121, and 40 : 25 is:
(A) 2 : 3
(B) 5 : 8
(C) 75 : 121
(D) 40 : 25

Solution:
To compare the ratios, we convert them to decimal form:
- \(2 : 3 = \frac{2}{3} \approx 0.6667\)
- \(5 : 8 = \frac{5}{8} = 0.625\)
- \(75 : 121 = \frac{75}{121} \approx 0.6199\)
- \(40 : 25 = \frac{40}{25} = 1.6\)

The largest value is \(1.6\), which corresponds to the ratio \(40 : 25\).

Answer: (D) 40 : 25

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Problem 9:

There are 'b' boys and 'g' girls in a class. The ratio of the number of boys to the total number of students in the class is:
(A) \(\frac{b}{b+g}\)
(B) \(\frac{g}{b+g}\)
(C) \(\frac{b}{g}\)
(D) \(\frac{b+g}{b}\)

Solution:
- Number of boys = \(b\)
- Number of girls = \(g\)
- Total number of students = \(b + g\)
The ratio of the number of boys to the total number of students is:
\[
\frac{\text{Number of boys}}{\text{Total number of students}} = \frac{b}{b+g}
\]

Answer: (A) \(\frac{b}{b+g}\)

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Problem 10:

If a bus travels 160 km in 4 hours and a train travels 320 km 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:
- Speed of the bus = \(\frac{\text{Distance}}{\text{Time}} = \frac{160}{4} = 40 \text{ km/h}\)
- Speed of the train = \(\frac{\text{Distance}}{\text{Time}} = \frac{320}{5} = 64 \text{ km/h}\)
The ratio of the distances travelled by the bus and the train in one hour is:
\[
\frac{\text{Speed of bus}}{\text{Speed of train}} = \frac{40}{64} = \frac{40 \div 8}{64 \div 8} = \frac{5}{8}
\]
Thus, the ratio is \(5 : 8\).

Answer: (C) 5 : 8

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Final Answers:

1. (A) 2 : 5
2. (D) 1 : 3
3. (D) 1 : 8
4. (B) 1 : 7
5. (C) 3 : 80
6. (D) 22
7. (C) 27
8. (D) 40 : 25
9. (A) \(\frac{b}{b+g}\)
10. (C) 5 : 8

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