CBSE Class 8 Mathematics Comparing Quantities Assignment Set 10

Ratio and Percentage:

Question 1(a). Find the ratio of 25P to 5 Rs
Answer: 1 Rs = 100 P
5 Rs = 5 \times 100 = 500 P
Ratio = \(\frac{25}{500} = \frac{1}{20}\) = 1:20
In simple words: Convert both quantities into the same unit (paise) before finding the ratio.

Exam Tip: Always make units identical (convert Rs to paise) before calculating ratios.

Question 1(b). Find the ratio of 10 cm to 1 km
Answer: 1 km = 1000 m = 1000 \times 100 cm = 100000 cm
Ratio = \(\frac{10}{100000} = \frac{1}{10000}\) = 1:10000
In simple words: Convert kilometers to centimeters by multiplying by 100,000.

Exam Tip: Remember standard conversions: 1 m = 100 cm and 1 km = 100000 cm.

Question 1(c). Find the ratio of 15 m to 15 km
Answer: 1 km = 1000 m
15 km = 15 \times 1000 = 15000 m
Ratio = \(\frac{15}{15000} = \frac{1}{1000}\) = 3:200 (Wait, 15/15000 simplifies to 1/1000 or 1:1000; note answer key lists 3:200 which is a typo in source source, let us provide correct reduction: \(\frac{15}{15000} = \frac{1}{1000}\))
In simple words: Convert both measurements to meters.

Exam Tip: Simplify fractions completely to lowest terms.

Question 2(a). Convert the ratio into percentage: 3:4
Answer: Ratio = \(\frac{3}{4}\)
Percentage = \(\frac{3}{4} \times 100\% = 3 \times 25\% = 75\%\)
In simple words: Multiply the fraction form of the ratio by 100.

Exam Tip: To convert any ratio or fraction to a percentage, multiply by 100 and add the percent sign.

Question 2(b). Convert the ratio into percentage: 2:3
Answer: Ratio = \(\frac{2}{3}\)
Percentage = \(\frac{2}{3} \times 100\% = \frac{200}{3}\% = 66\frac{2}{3}\%\)
In simple words: Divide 200 by 3 to get the mixed fraction percentage.

Question 3(a). Convert the percentage into fractions: 75%
Answer: \(75\% = \frac{75}{100}\)
Dividing numerator and denominator by 25: \(\frac{75 \div 25}{100 \div 25} = \frac{3}{4}\)
In simple words: Remove the percent sign and divide the number by 100.

Exam Tip: Always reduce the fraction to its simplest form.

Question 3(b). Convert the percentage into fractions: 50%
Answer: \(50\% = \frac{50}{100} = \frac{1}{2}\)
In simple words: 50 percent means half of a whole.

Exam Tip: 50% always simplifies to 1/2.

Question 4(a). Convert the percentage into decimals: 75%
Answer: \(75\% = \frac{75}{100} = 0.75\)
In simple words: Move the decimal point two places to the left.

Exam Tip: Dividing by 100 shifts the decimal point two places left.

Question 4(b). Convert the percentage into decimals: 25%
Answer: \(25\% = \frac{25}{100} = 0.25\)
In simple words: 25 percent written as a decimal is 0.25.

Exam Tip: Keep two decimal places for percentages out of 100.

Question 5(a). Convert 28% in ratio
Answer: \(28\% = \frac{28}{100}\)
Divide numerator and denominator by 4: \(\frac{28 \div 4}{100 \div 4} = \frac{7}{25}\) = 7:25
In simple words: Express the percentage as a fraction and write it as a ratio.

Exam Tip: A fraction a/b is written as ratio a:b.

Question 5(b). Convert 72% in ratio
Answer: \(72\% = \frac{72}{100}\)
Divide numerator and denominator by 4: \(\frac{72 \div 4}{100 \div 4} = \frac{18}{25}\) = 18:25
In simple words: Simplify 72/100 by dividing by their common factor 4.

Exam Tip: Find the highest common factor (HCF) to simplify quickly.

Question 6(a). Express \(15\frac{1}{2}\%\) into fraction
Answer: \(15\frac{1}{2}\% = \frac{31}{2}\% = \frac{31}{2 \times 100} = \frac{31}{200}\)
In simple words: Convert the mixed fraction to an improper fraction and divide by 100.

Exam Tip: Multiply the denominator of the percent by 100.

Question 6(b). Express \(3\frac{1}{4}\) into percent
Answer: \(3\frac{1}{4} = \frac{13}{4}\)
Percentage = \(\frac{13}{4} \times 100\% = 13 \times 25\% = 325\%\) (Note: source answer key prints 1300/4 %, which equals 325%)
In simple words: Multiply the mixed number by 100 to find the percentage.

Exam Tip: Convert mixed numbers to improper fractions first.

Question 6(c). Express 225% into decimals
Answer: \(225\% = \frac{225}{100} = 2.25\)
In simple words: Divide 225 by 100 by moving the decimal point two places left.

Exam Tip: Percentages greater than 100 convert to decimals greater than 1.

Question 6(d). Express 2:3 into percent
Answer: Ratio = \(\frac{2}{3}\)
Percentage = \(\frac{2}{3} \times 100\% = \frac{200}{3}\% = 66\frac{2}{3}\%\)
In simple words: Multiply the fraction by 100 and simplify.

Exam Tip: Same method as Question 2(b).

Question 7. Find 75% of 225.
Answer: \(75\% \text{ of } 225 = \frac{75}{100} \times 225 = \frac{3}{4} \times 225 = \frac{675}{4} = 168\frac{3}{4}\)
In simple words: Multiply 225 by 75/100.

Exam Tip: Reduce fractions before multiplying to save time.

Question 8. What % of 45 is 60?
Answer: Let required percentage be \(x\%\)
\(x\% \text{ of } 45 = 60\)
\(\frac{x}{100} \times 45 = 60\)
\(x = \frac{60 \times 100}{45} = \frac{6000}{45} = \frac{400}{3} = 133\frac{1}{3}\%\)
In simple words: Divide the part (60) by the whole (45) and multiply by 100.

Exam Tip: Formula: (Part / Whole) * 100.

Question 9. 30% of what number is 60?
Answer: Let the number be \(y\)
\(30\% \text{ of } y = 60\)
\(\frac{30}{100} \times y = 60\)
\(y = \frac{60 \times 100}{30} = 2 \times 100 = 200\)
In simple words: Multiply 60 by the reciprocal of 30/100.

Exam Tip: Translate "of" as multiplication and "is" as equals.

Question 10. Find \(x\) if \(\frac{3}{2}\%\) of \(x\) is 15.
Answer: \(\frac{3}{2}\% \text{ of } x = 15\)
\(\frac{3}{2 \times 100} \times x = 15\)
\(\frac{3}{200} \times x = 15\)
\(x = \frac{15 \times 200}{3} = 5 \times 200 = 1000\)
In simple words: Convert the percentage to a fraction 3/200 and solve for x.

Exam Tip: Isolate \(x\) by multiplying both sides by the reciprocal.