SCERT Solutions for Class 7 Maths Chapter 8 Comparing Quantities Exercise 8.2

Free Solutions for Assam State Board Class 7 Maths Chapter 8 Exercise 8.2 in English Medium

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1. Express the following fraction in percentage
(তলৰ ভগ্নাংশবোৰক শতাংশত প্ৰকাশ কৰা।)

(i) $\frac{3}{5}$

Solution:
$\frac{3}{5} \times 100\% = 3 \times 20\% = 60\%$

(ii) $\frac{7}{12}$

Solution:
$\frac{7}{12} \times 100\% = \frac{700}{12}\% = 58.33\%$

(iii) $\frac{15}{32}$

Solution:
$\frac{15}{32} \times 100\% = \frac{1500}{32}\% = 46.875\%$

(iv) $\frac{13}{25}$

Solution:
$\frac{13}{25} \times 100\% = 13 \times 4\% = 52\%$

(v) $\frac{21}{40}$

Solution:
$\frac{21}{40} \times 100\% = \frac{2100}{40}\% = 52.5\%$

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2. Express the decimal fraction in percentage
(তলৰ দশমিক ভগ্নাংশবোৰক শতাংশত প্ৰকাশ কৰা।)

(i) $0.8$

Solution:
$0.8 \times 100\% = 80\%$

(ii) $5.75$

Solution:
$5.75 \times 100\% = 575\%$

(iii) $0.08$

Solution:
$0.08 \times 100\% = 8\%$

(iv) $32.1$

Solution:
$32.1 \times 100\% = 3210\%$

(v) $0.004$

Solution:
$0.004 \times 100\% = 0.4\%$

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3. Express in fraction
(ভগ্নাংশত প্ৰকাশ কৰা।)

(i) $20\%$

Solution:
$20\% = \frac{20}{100} = \frac{1}{5}$

(ii) $32\%$

Solution:
$32\% = \frac{32}{100} = \frac{8}{25}$

(iii) $0.5\%$

Solution:
$0.5\% = \frac{0.5}{100} = \frac{1}{200}$

(iv) $7.25\%$

Solution:
$7.25\% = \frac{7.25}{100} = \frac{725}{10000} = \frac{29}{400}$

(v) $180\%$

Solution:
$180\% = \frac{180}{100} = \frac{9}{5}$

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4. Convert the percentages into decimal fraction and express the fraction in the lowest form:

(তলত দিয়া শতাংশ বোৰক দশমিক ভগ্নাংশলৈ আৰু লগিষ্ঠ ভগ্নাংশলৈ পৰিবৰ্তন কৰা।)

(i) 18%
Solution:

$$18\% = \frac{18}{100} = 0.18$$

Again:

$$0.18 = \frac{18}{100} = \frac{9}{50}$$

(ii) 0.25%
Solution:

$$0.25\% = \frac{0.25}{100} = 0.0025$$

Again:

$$0.0025 = \frac{25}{10000} = \frac{1}{4000}$$

(iii) 60%
Solution:

$$60\% = \frac{60}{100} = 0.60$$

Again:

$$0.60 = \frac{60}{100} = \frac{3}{5}$$

(iv) 42.5%
Solution:

$$42.5\% = \frac{42.5}{100} = 0.425$$

Again:

$$0.425 = \frac{425}{1000} = \frac{17}{40}$$

(v) 56%
Solution:

$$56\% = \frac{56}{100} = 0.56$$

Again:

$$0.56 = \frac{56}{100} = \frac{14}{25}$$

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5. Express in percentage:

(শতাংশত প্ৰকাশ কৰা।)

(i) $4:10$
Solution:

$$\frac{4}{10} \times 100\% = 40\%$$

(ii) $11:20$
Solution:

$$\frac{11}{20} \times 100\% = 55\%$$

(iii) $19:50$
Solution:

$$\frac{19}{50} \times 100\% = 38\%$$

(iv) $3:25$
Solution:

$$\frac{3}{25} \times 100\% = 12\%$$

(v) $9:4$
Solution:

$$\frac{9}{4} \times 100\% = 225\%$$

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6. Express in ratio:

(অনুপাতত প্ৰকাশ কৰা।)

(i) $72\%$
Solution:

$$72\% = \frac{72}{100} = \frac{18}{25} = 18:25$$

(ii) $0.25\%$
Solution:

$$0.25\% = \frac{0.25}{100} = \frac{1}{400} = 1:400$$

(iii) $0.14\%$
Solution:

$$0.14\% = \frac{0.14}{100} = \frac{7}{5000} = 7:5000$$

(iv) $6\%$
Solution:

$$6\% = \frac{6}{100} = \frac{3}{50} = 3:50$$

(v) $4.6\%$
Solution:

$$4.6\% = \frac{4.6}{100} = \frac{23}{500} = 23:500$$

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7. Express the coloured portion of the following figures in percentage( তলৰ চিত্ৰবোৰৰ ৰং কৰা অংশক শতাংশত প্ৰকাশ কৰা।)

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 (i)

Solution:

$$\frac{1}{4} \times 100\% = 25\%$$

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(ii)

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Solution:

$$\frac{\left(\frac{1}{2}\right)}{3} \times 100\% = \frac{1}{2} \times \frac{1}{3} \times 100\% = \frac{50}{3}\% = 16 \frac{2}{3}\%$$

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(iii) 

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Solution:

$$\frac{12}{40} \times 100\% = 30\%$$

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8. Express in percentage:

(শতাংশত প্ৰকাশ কৰা।)

(i) 8 hours of a day
Solution:

$$\frac{8}{24} \times 100\% = 33 \frac{1}{3}\%$$

(ii) 72 persons out of 80
Solution:

$$\frac{72}{80} \times 100\% = 90\%$$

(iii) 25 Paisa of Rs 5
Solution:

$$\frac{25}{500} \times 100\% = 5\%$$

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9. Determine the value:

(মান নিৰ্ণয় কৰা)

(i) 20% of 50
Solution:

$$50 \times \frac{20}{100} = 10$$

(ii) 30% of 600
Solution:

$$600 \times \frac{30}{100} = 180$$

(iii) 20% of 5 km
Solution:

$$5 \times \frac{20}{100} = 1 \, \text{km}$$

(iv) 30% of 1 hour
Solution:

$$60 \times \frac{30}{100} \, \text{minutes} = 18 \, \text{minutes}$$

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Questions No. 10: If 20% of a number is 50, determine the number.

(এটা সংখ্যাৰ 20% ৰ মান 50 হ'লে সংখ্যাটো নিৰ্ণয় কৰা।)

Solution:
Let the number be $X$.

According to the question:

$$20\% \, \text{of} \, X = 50$$ $$\frac{20}{100} \times X = 50$$ $$X = 50 \times \frac{100}{20} = 250$$

The required number is 250.

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Question No. 11: 13% of which number is 91?

(কি সংখ্যাৰ 13% ৰ মান 91 হব?)

Solution:
Let the number be $X$.

According to the question:

$$13\% \, \text{of} \, X = 91$$ $$\frac{13}{100} \times X = 91$$ $$X = 91 \times \frac{100}{13} = 700$$

The required number is 700.

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Question No. 12: What percentage of ₹40 is ₹16?

(₹40 টকাৰ কিমান শতাংশৰ মান ₹16 হ'ব?)

Solution:
Let the percentage be $X\%$.

According to the question:

$$X\% \, \text{of} \, 40 = 16$$ $$\frac{X}{100} \times 40 = 16$$ $$X = 16 \times \frac{100}{40} = 40\%$$

The required percentage is 40%.

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Question No. 13: Express "30 out of 40" and "40 out of 50" in percentage. Which is greater?

(“40 ৰ ভিতৰত 30” আৰু “50 ৰ ভিতৰত 40” দুয়োটাকৈ শতাংশত প্ৰকাশ কৰা। দুয়োটাৰ কোনটো বেছি?)

Solution:
For "30 out of 40":

$$\frac{30}{40} \times 100\% = 75\%$$

For "40 out of 50":

$$\frac{40}{50} \times 100\% = 80\%$$

Now, 40 out of 50 (80%) is greater than 30 out of 40 (75%).

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Question No. 14: The area of a garden is 400 square meter. The garden is arranged in the following manner

( এখন বাগিচাৰ কালি 400 বৰ্গ মিটাৰ । তলৰ দিয়া ধৰণৰ বাগিচাৰ খন সজোৱা হৈছিল।)

(i) Find the area of the space for flowers if 30% of a 400 sq. m garden is reserved for flowers.

(ফুলৰ বাবে বাগিচা খনৰ 30% ঠাই ৰখা হৈছে। ফুল থকা ঠাইৰ কালি উলিওৱা।)

Solution:
The area of the garden = 400 sq. m.
30% of the garden is reserved for flowers.

$$\text{Area for flowers} = 30\% \, \text{of} \, 400 \, \text{sq.m}$$ $$\frac{30}{100} \times 400 = 120 \, \text{sq.m}$$

The area of space for flowers is 120 sq. m.

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(ii) The area of a pond in the garden is 80 sq. m. What percentage of the garden is covered by the pond?

(বাগিচাৰ খনত থকা পুখুৰীটোৱে কিমান শতাংশ ঠাই আগুৰি লৈছে?)

Solution:
The area of the garden = 400 sq. m.
The area of the pond = 80 sq. m.

$$\text{Percentage covered by pond} = \frac{80}{400} \times 100$$ $$= 20\%$$

The pond covers 20% of the garden.

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