CBSE Class 6 Maths Chapter 8: Ratio and Proportion NCERT Solutions

To find the ratio of 8 books to 20 books, we write it as a fraction:

$$\backslash frac\{8\}\{20\}$$

Now, we simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 4:

$$\backslash frac\{8\; \backslash div\; 4\}\{20\; \backslash div\; 4\}\; =\; \backslash frac\{2\}\{5\}$$

Therefore, the ratio of 8 books to 20 books is 2:5. Option (A) is the correct answer.

First, let's identify the number of sides of a square and the number of edges of a cube.

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:

$$\backslash frac\{\backslash text\{Number\; of\; sides\; of\; a\; square\}\}\{\backslash text\{Number\; of\; edges\; of\; a\; cube\}\}\; =\; \backslash frac\{4\}\{12\}$$

To simplify this ratio, we divide both numbers by their greatest common divisor, which is 4:

$$\backslash frac\{4\; \backslash div\; 4\}\{12\; \backslash div\; 4\}\; =\; \backslash frac\{1\}\{3\}$$

So, the ratio is 1:3. Option (D) is the correct answer.

We are given the width of the picture as 60 cm. The length is given as 1.8 m. To calculate the perimeter, both dimensions must be in the same unit. Let's convert the length to centimeters:

Length = 1.8 m = 1.8 \(\times\) 100 cm = 180 cm.

The formula for the perimeter of a rectangle is P = 2(length + width).

Perimeter = $2(180\; \backslash text\{\; cm\}\; +\; 60\; \backslash text\{\; cm\})$

Perimeter = $2(240\; \backslash text\{\; cm\})$

Perimeter = $480\; \backslash text\{\; cm\}$

Now, we need to find the ratio of the width to the perimeter in its lowest form. The width is 60 cm and the perimeter is 480 cm.

Ratio = $\backslash frac\{\backslash text\{Width\}\}\{\backslash text\{Perimeter\}\}\; =\; \backslash frac\{60\; \backslash text\{\; cm\}\}\{480\; \backslash text\{\; cm\}\}$

To simplify the ratio, we can divide both numbers by 10:

$\backslash frac\{60\}\{480\}\; =\; \backslash frac\{6\}\{48\}$

Now, we divide both by their greatest common divisor, which is 6:

$\backslash frac\{6\; \backslash div\; 6\}\{48\; \backslash div\; 6\}\; =\; \backslash frac\{1\}\{8\}$

So, the ratio of the width to its perimeter in the lowest form is 1:8. Option (D) is the correct answer.

Neelam's annual income is Rs. 288000.

Her annual savings are Rs. 36000.

To find the ratio of savings to expenditure, we first need to calculate her expenditure. Expenditure is the income minus the savings.

Expenditure = Annual Income - Annual Savings

Expenditure = Rs. 288000 - Rs. 36000

Expenditure = Rs. 252000

Now, we find the ratio of her savings to her expenditure:

Ratio = $\backslash frac\{\backslash text\{Savings\}\}\{\backslash text\{Expenditure\}\}\; =\; \backslash frac\{36000\}\{252000\}$

To simplify this ratio, we can cancel out the zeros and then find the greatest common divisor. Let's divide both by 1000:

$\backslash frac\{36\}\{252\}$

Now, we find the greatest common divisor of 36 and 252. We can see that 252 is divisible by 36 (252 = 36 \(\times\) 7).

So, we divide both by 36:

$\backslash frac\{36\; \backslash div\; 36\}\{252\; \backslash div\; 36\}\; =\; \backslash frac\{1\}\{7\}$

The ratio of her savings to her expenditure is 1:7. Option (B) is the correct answer.

The total number of pages in the Mathematics textbook is 320.

The chapter 'Symmetry' starts on page 261 and ends on page 272.

To find the number of pages in the chapter, we include both the starting and ending pages. The formula is (Last Page - First Page) + 1.

Number of pages in 'Symmetry' chapter = $(272\; -\; 261)\; +\; 1$

Number of pages = $11\; +\; 1\; =\; 12$

Now, we need to find the ratio of the number of pages of this chapter to the total number of pages of the book.

Ratio = $\backslash frac\{\backslash text\{Number\; of\; pages\; in\; chapter\}\}\{\backslash text\{Total\; number\; of\; pages\}\}\; =\; \backslash frac\{12\}\{320\}$

To simplify this ratio, we find the greatest common divisor of 12 and 320. Both numbers are divisible by 4.

$\backslash frac\{12\; \backslash div\; 4\}\{320\; \backslash div\; 4\}\; =\; \backslash frac\{3\}\{80\}$

So, the ratio of the number of pages of the 'Symmetry' chapter to the total number of pages of the book is 3:80. Option (C) is the correct answer.