CBSE Class 7 Maths Exemplar Chapter 7: Comparing Quantities NCERT Solutions

To calculate 20% of 700 meters, we can use the formula for percentage:

$$\backslash text\{Percentage\}\; =\; \backslash frac\{\backslash text\{Part\}\}\{\backslash text\{Whole\}\}\; \backslash times\; 100$$

In this case, we want to find the 'part' which is 20% of 700 m. We can rewrite the percentage as a fraction:

$$20\backslash \%\; =\; \backslash frac\{20\}\{100\}$$

Now, we multiply this fraction by the total amount (700 m):

$$\backslash frac\{20\}\{100\}\; \backslash times\; 700\; \backslash text\{\; m\}\; =\; \backslash frac\{20\; \backslash times\; 700\}\{100\}\; \backslash text\{\; m\}$$

We can simplify this calculation:

$$\backslash frac\{14000\}\{100\}\; \backslash text\{\; m\}\; =\; 140\; \backslash text\{\; m\}$$

Therefore, 20% of 700 m is 140 m. The correct option is (d).

Gayatri's annual income is ₹ 160000.

First, calculate the amount spent on house rent:

House rent = 15% of ₹ 160000

$$\backslash text\{House\; rent\}\; =\; \backslash frac\{15\}\{100\}\; \backslash times\; 160000\; =\; 15\; \backslash times\; 1600\; =\; \backslash text\{₹\; \}\; 24000$$

Next, find the amount of income remaining after paying house rent:

$$\backslash text\{Remaining\; amount\}\; =\; \backslash text\{Income\}\; -\; \backslash text\{House\; rent\}$$

$$\backslash text\{Remaining\; amount\}\; =\; 160000\; -\; 24000\; =\; \backslash text\{₹\; \}\; 136000$$

Now, calculate the amount spent on her child's education, which is 10% of the *remainder*:

Expenditure on child's education = 10% of ₹ 136000

$$\backslash text\{Expenditure\}\; =\; \backslash frac\{10\}\{100\}\; \backslash times\; 136000\; =\; \backslash frac\{1360000\}\{100\}\; =\; \backslash text\{₹\; \}\; 13600$$

Finally, calculate the total money left with her after both expenses:

$$\backslash text\{Money\; left\}\; =\; \backslash text\{Remaining\; amount\}\; -\; \backslash text\{Expenditure\; on\; education\}$$

$$\backslash text\{Money\; left\}\; =\; 136000\; -\; 13600\; =\; \backslash text\{₹\; \}\; 122400$$

Alternatively, we can calculate the total expenses and subtract from the income:

$$\backslash text\{Total\; expenses\}\; =\; \backslash text\{House\; rent\}\; +\; \backslash text\{Expenditure\; on\; education\}\; =\; 24000\; +\; 13600\; =\; \backslash text\{₹\; \}\; 37600$$

$$\backslash text\{Money\; left\}\; =\; \backslash text\{Income\}\; -\; \backslash text\{Total\; expenses\}\; =\; 160000\; -\; 37600\; =\; \backslash text\{₹\; \}\; 122400$$

Hence, the money left with her is ₹ 122400. The correct option is (c).

The problem states that the ratio of Fatima's income to her savings is 4:1. This means that for every ₹4 of income, she saves ₹1.

Let Fatima's income be represented by $4x$ and her savings by $x$, where $x$ is a common factor.

To find the percentage of money saved, we use the formula:

$$\backslash text\{Savings\; Percentage\}\; =\; \backslash frac\{\backslash text\{Savings\}\}\{\backslash text\{Income\}\}\; \backslash times\; 100\backslash \%$$

Substitute the given ratio values:

$$\backslash text\{Savings\; Percentage\}\; =\; \backslash frac\{x\}\{4x\}\; \backslash times\; 100\backslash \%$$

The $x$ terms cancel out:

$$\backslash text\{Savings\; Percentage\}\; =\; \backslash frac\{1\}\{4\}\; \backslash times\; 100\backslash \%$$

Calculating the value:

$$\backslash text\{Savings\; Percentage\}\; =\; 25\backslash \%$$

Therefore, the percentage of money saved by Fatima is 25%. The correct option is (b).

To convert a decimal to a percentage, we multiply the decimal by 100 and add the '%' sign.

The given decimal is 0.07.

Multiply by 100:

$$0.07\; \backslash times\; 100\; =\; 7$$

So, 0.07 is equal to 7%.

Alternatively, we can express the decimal as a fraction with a denominator of 100:

$$0.07\; =\; \backslash frac\{7\}\{100\}$$

Since 'percent' means 'out of one hundred', $\backslash frac\{7\}\{100\}$ is directly equal to 7%.

Hence, the correct option is (b).

Let's assume the total number of scouts in the camp is 100 for easier calculation.

Number of scouts from Gujarat = 40% of 100

$$\backslash text\{Scouts\; from\; Gujarat\}\; =\; \backslash frac\{40\}\{100\}\; \backslash times\; 100\; =\; 40$$

Now, we are told that 20% of these scouts from Gujarat were from Ahmedabad.

Number of scouts from Ahmedabad = 20% of the scouts from Gujarat

$$\backslash text\{Scouts\; from\; Ahmedabad\}\; =\; \backslash frac\{20\}\{100\}\; \backslash times\; 40$$

$$\backslash text\{Scouts\; from\; Ahmedabad\}\; =\; \backslash frac\{800\}\{100\}\; =\; 8$$

To find the percentage of scouts in the *entire camp* who are from Ahmedabad, we compare the number of scouts from Ahmedabad to the total number of scouts in the camp:

$$\backslash text\{Percentage\; from\; Ahmedabad\}\; =\; \backslash frac\{\backslash text\{Number\; of\; scouts\; from\; Ahmedabad\}\}\{\backslash text\{Total\; number\; of\; scouts\}\}\; \backslash times\; 100\backslash \%$$

$$\backslash text\{Percentage\; from\; Ahmedabad\}\; =\; \backslash frac\{8\}\{100\}\; \backslash times\; 100\backslash \%$$

$$\backslash text\{Percentage\; from\; Ahmedabad\}\; =\; 8\backslash \%$$

Therefore, 8% of the scouts in the camp are from Ahmedabad. The correct option is (c).

We need to find what percentage of ₹ 4500 is equal to ₹ 9000. Let this percentage be 'P'.

We can set up the equation based on the definition of percentage:

$$P\backslash \%\; \backslash text\{\; of\; \}\; 4500\; =\; 9000$$

Writing the percentage as a fraction:

$$\backslash frac\{P\}\{100\}\; \backslash times\; 4500\; =\; 9000$$

Now, we solve for P. First, simplify the left side:

$$P\; \backslash times\; \backslash frac\{4500\}\{100\}\; =\; 9000$$

$$P\; \backslash times\; 45\; =\; 9000$$

To find P, divide 9000 by 45:

$$P\; =\; \backslash frac\{9000\}\{45\}$$

We can simplify this division. Notice that 90 is 2 times 45:

$$P\; =\; \backslash frac\{90\; \backslash times\; 100\}\{45\}$$

$$P\; =\; 2\; \backslash times\; 100$$

$$P\; =\; 200$$

So, 200% of ₹ 4500 is ₹ 9000. The correct option is (a).