CBSE Class 8 Maths Chapter 8: Ratios and Percentages NCERT Solutions

To find the ratio, we need to express the quantities in the same units and then simplify.

1. Speed of cycle = 15 km/hr Speed of scooter = $30\; \backslash text\{\; km/hr\}$

   The ratio of the speed of the cycle to the speed of the scooter is:

   $$\backslash frac\{\backslash text\{Speed\; of\; cycle\}\}\{\backslash text\{Speed\; of\; scooter\}\}\; =\; \backslash frac\{15\; \backslash text\{\; km/hr\}\}\{30\; \backslash text\{\; km/hr\}\}\; =\; \backslash frac\{15\}\{30\}$$

   Simplifying the fraction by dividing both numerator and denominator by 15:

   $$\backslash frac\{15\}\{30\}\; =\; \backslash frac\{1\}\{2\}$$

   Therefore, the ratio is 1:2.

2. Distance 1 = 50 m Distance 2 = 10 km

   First, convert kilometers to meters. We know that $1\; \backslash text\{\; km\}\; =\; 1000\; \backslash text\{\; m\}$.

   So, 10 km = $10\; \backslash times\; 1000\; \backslash text\{\; m\}\; =\; 10000\; \backslash text\{\; m\}$.

   Now, find the ratio of 50 m to 10000 m:

   $$\backslash text\{Ratio\}\; =\; \backslash frac\{50\; \backslash text\{\; m\}\}\{10000\; \backslash text\{\; m\}\}\; =\; \backslash frac\{50\}\{10000\}$$

   Simplifying the fraction by dividing both numerator and denominator by 50:

   $$\backslash frac\{50\}\{10000\}\; =\; \backslash frac\{1\}\{200\}$$

   Therefore, the ratio is 1:200.

3. Amount 1 = 50 paise Amount 2 = ₹ 5

   First, convert rupees to paise. We know that $₹\; 1\; =\; 100\; \backslash text\{\; paise\}$.

   So, ₹ 5 = $5\; \backslash times\; 100\; \backslash text\{\; paise\}\; =\; 500\; \backslash text\{\; paise\}$.

   Now, find the ratio of 50 paise to 500 paise:

   $$\backslash text\{Ratio\}\; =\; \backslash frac\{50\; \backslash text\{\; paise\}\}\{500\; \backslash text\{\; paise\}\}\; =\; \backslash frac\{50\}\{500\}$$

   Simplifying the fraction by dividing both numerator and denominator by 50:

   $$\backslash frac\{50\}\{500\}\; =\; \backslash frac\{1\}\{10\}$$

   Therefore, the ratio is 1:10.

To convert a ratio to a percentage, we first express the ratio as a fraction and then multiply by 100%.

1. For the ratio 3:4, the fraction is $\backslash frac\{3\}\{4\}$. To convert this to a percentage:

   $$\backslash frac\{3\}\{4\}\; \backslash times\; 100\backslash \%\; =\; 75\backslash \%$$

   So, 3:4 is equal to 75%.
2. For the ratio 2:3, the fraction is $\backslash frac\{2\}\{3\}$. To convert this to a percentage:

   $$\backslash frac\{2\}\{3\}\; \backslash times\; 100\backslash \%\; =\; \backslash frac\{200\}\{3\}\backslash \%$$

   This can be expressed as a mixed number: $66\; \backslash frac\{2\}\{3\}\backslash \%$.

   So, 2:3 is equal to $66\; \backslash frac\{2\}\{3\}\backslash \%$.

The total number of students is given as 25.

The percentage of students who are good in mathematics is 72%.

First, let's calculate the number of students who are good in mathematics:

$$\backslash text\{Number\; of\; good\; students\}\; =\; 72\backslash \%\; \backslash text\{\; of\; \}\; 25\; =\; \backslash frac\{72\}\{100\}\; \backslash times\; 25$$

We can simplify this calculation:

$$\backslash frac\{72\}\{100\}\; \backslash times\; 25\; =\; \backslash frac\{72\}\{4\}\; =\; 18$$

So, 18 students are good in mathematics.

To find the number of students who are not good in mathematics, subtract the number of good students from the total number of students:

$$\backslash text\{Number\; of\; students\; not\; good\}\; =\; \backslash text\{Total\; students\}\; -\; \backslash text\{Number\; of\; good\; students\}$$

$$=\; 25\; -\; 18\; =\; 7$$

Therefore, 7 students are not good in mathematics.

Alternatively, we can find the percentage of students not good in mathematics first: $100\backslash \%\; -\; 72\backslash \%\; =\; 28\backslash \%$. Then calculate 28% of 25: $\backslash frac\{28\}\{100\}\; \backslash times\; 25\; =\; \backslash frac\{28\}\{4\}\; =\; 7$.

Let the total number of matches played by the football team be $x$.

We are given that the team won 10 matches, and their win percentage was 40%.

This means that 40% of the total matches played ($x$) is equal to 10 matches.

We can write this as an equation:

$$40\backslash \%\; \backslash text\{\; of\; \}\; x\; =\; 10$$

Converting the percentage to a fraction:

$$\backslash frac\{40\}\{100\}\; \backslash times\; x\; =\; 10$$

Now, we solve for $x$:

$$x\; =\; \backslash frac\{10\; \backslash times\; 100\}\{40\}$$

Simplify the expression:

$$x\; =\; \backslash frac\{1000\}\{40\}\; =\; \backslash frac\{100\}\{4\}\; =\; 25$$

Therefore, the football team played a total of 25 matches.

Let the amount of money Chameli had in the beginning be $₹\; x$.

She spent 75% of her money. This means the percentage of money she has left is:

$$100\backslash \%\; -\; 75\backslash \%\; =\; 25\backslash \%$$

We are told that she had ₹ 600 left. So, 25% of her initial money ($x$) is equal to ₹ 600.

We can write this as an equation:

$$25\backslash \%\; \backslash text\{\; of\; \}\; x\; =\; 600$$

Converting the percentage to a fraction:

$$\backslash frac\{25\}\{100\}\; \backslash times\; x\; =\; 600$$

Simplify the fraction $\backslash frac\{25\}\{100\}$ to $\backslash frac\{1\}\{4\}$:

$$\backslash frac\{1\}\{4\}\; \backslash times\; x\; =\; 600$$

Now, solve for $x$ by multiplying both sides by 4:

$$x\; =\; 600\; \backslash times\; 4$$

$$x\; =\; 2400$$

Therefore, Chameli had ₹ 2400 in the beginning.