Samacheer Kalvi Class 8 Maths Solutions Chapter 4 Life Mathematics Exercise 4.1

Tamilnadu Samacheer Kalvi 8th Maths Solutions Chapter 4 Life Mathematics Ex 4.1

Question 1. Fill in the blanks:
(i) If 30 % of x is 150, then x is _________.
Answer:
To find x, we know that 30% of x is 150. This means \( \frac { 30 }{ 100 } \times x = 150 \). To get x alone, we can move the fraction to the other side by multiplying by its inverse.
\( x = \frac { 150 \times 100 }{ 30 } \)
\( x = 5 \times 100 \)
\( x = 500 \)
So, the number x is 500. This calculation helps us find the whole amount when we only know a part of it.
In simple words: If 30 percent of a number is 150, that number is 500. We found it by dividing 150 by 30% (or 0.30).

🎯 Exam Tip: When finding the whole from a percentage, remember to divide the given part by the percentage (expressed as a decimal or fraction).

(ii) 2 minutes is _________ % to an hour.
Answer:
First, we need to know that 1 hour has 60 minutes. We want to find out what percentage 2 minutes is of 60 minutes. We can write this as a fraction: \( \frac { 2 }{ 60 } \). To turn this fraction into a percentage, we multiply it by 100.
Percentage \( = \frac { 2 }{ 60 } \times 100 \)
\( = \frac { 1 }{ 30 } \times 100 \)
\( = \frac { 10 }{ 3 } \)
\( = 3\frac{1}{3} \% \)
So, 2 minutes is \( 3\frac{1}{3} \% \) of an hour. Understanding time units is key in these types of problems.
In simple words: Two minutes is \( 3\frac{1}{3} \% \) of one hour. We calculated it by dividing 2 by 60 and then multiplying by 100.

🎯 Exam Tip: Always make sure the units are the same (e.g., minutes and minutes) before calculating percentages or ratios.

(iii) If x% of x = 25, then x = _________.
Answer:
The problem states that x% of x is 25. We can write x% as \( \frac { x }{ 100 } \).
So, the equation becomes \( \frac { x }{ 100 } \times x = 25 \).
This simplifies to \( \frac { x^2 }{ 100 } = 25 \).
To find \( x^2 \), we multiply both sides by 100: \( x^2 = 25 \times 100 = 2500 \).
Now, we need to find the square root of 2500 to get x.
\( x = \sqrt{2500} \)
\( x = 50 \)
Therefore, x is 50. This is a good example of working with percentages and squares.
In simple words: If x percent of x equals 25, then x is 50. We found this by setting up an equation and solving for x.

🎯 Exam Tip: Remember that "x percent" means \( \frac{x}{100} \). This is a common mistake when solving percentage-based equations.

(iv) In a school of 1400 students, there are 420 girls. The percentage of boys in the school is _________.
Answer:
First, we need to find the number of boys in the school. The total number of students is 1400, and there are 420 girls.
Number of boys = Total students - Number of girls
Number of boys = \( 1400 - 420 = 980 \)
Now, to find the percentage of boys, we divide the number of boys by the total number of students and multiply by 100.
Percentage of boys = \( \frac { \text{Number of boys} }{ \text{Total number of students} } \times 100 \)
Percentage of boys = \( \frac { 980 }{ 1400 } \times 100 \)
Percentage of boys = \( \frac { 98 }{ 140 } \times 100 \)
Percentage of boys = \( \frac { 98 }{ 14 } \times 10 \)
Percentage of boys = \( 7 \times 10 = 70\% \)
So, 70% of the students in the school are boys. This shows how percentages help understand proportions within a group.
In simple words: There are 980 boys in the school. To find their percentage, we divide 980 by the total students (1400) and multiply by 100, which gives 70%.

🎯 Exam Tip: When calculating percentages of a group, first find the number of items in that specific group, then divide by the total and multiply by 100.

(v) 0.5252 is _________ %.
Answer:
To express a decimal as a percentage, we simply multiply the decimal by 100. This is because "percent" means "per hundred".
Percentage = \( 0.5252 \times 100 \)
Percentage = \( 52.52\% \)
So, 0.5252 is 52.52%. Moving the decimal point two places to the right is a quick way to do this.
In simple words: To change 0.5252 into a percentage, you multiply it by 100, which gives 52.52%.

🎯 Exam Tip: Converting decimals to percentages simply involves multiplying by 100 and adding the percent symbol.

Question 2. Rewrite each underlined part using percentage language.
(i) One half of the cake is distributed to the children.
Answer:
"One half" can be written as the fraction \( \frac { 1 }{ 2 } \). To express this as a percentage, we multiply by 100.
Percentage = \( \frac { 1 }{ 2 } \times 100\% = 50\% \)
So, the sentence becomes: 50% of the cake is distributed to the children. Percentages help to clearly express parts of a whole.
In simple words: "One half" means 50 percent. So, 50% of the cake was given to the children.

🎯 Exam Tip: Common fractions like half, quarter, and three-quarters should be easily convertible to their percentage equivalents (50%, 25%, 75%).

(ii) Aparna scored 7.5 points out of 10 in a competition.
Answer:
Aparna's score can be written as a fraction: \( \frac { 7.5 }{ 10 } \). To convert this score into a percentage, we multiply by 100.
Percentage = \( \frac { 7.5 }{ 10 } \times 100\% \)
Percentage = \( 0.75 \times 100\% = 75\% \)
So, Aparna scored 75% in a competition. This clearly shows her performance relative to the maximum possible score.
In simple words: Aparna got 7.5 points out of 10. This means she scored 75 percent in the competition.

🎯 Exam Tip: To convert a score or fraction to a percentage, divide the part by the total and multiply by 100.

(iii) The statue was made of pure silver.
Answer:
When something is described as "pure," it means it is 100% of that material and contains no other elements.
So, the sentence becomes: The statue was made of 100% pure silver. This is the highest possible purity.
In simple words: If a statue is made of "pure" silver, it means it is 100 percent silver.

🎯 Exam Tip: "Pure" always implies 100% composition of the specified material.

(iv) 48 out of 50 students participated in sports.
Answer:
We have 48 students out of a total of 50. To find this as a percentage, we divide 48 by 50 and then multiply by 100.
Percentage = \( \frac { 48 }{ 50 } \times 100\% \)
Percentage = \( 0.96 \times 100\% = 96\% \)
So, 96% of students participated in sports. This is a very high participation rate.
In simple words: 48 out of 50 students joined sports. This is 96 percent of all students.

🎯 Exam Tip: Always make sure to divide the part by the total to get the fraction before multiplying by 100 for the percentage.

(v) Only 2 persons out of 3 will be selected in the interview.
Answer:
The fraction of selected persons is \( \frac { 2 }{ 3 } \). To convert this into a percentage, we multiply by 100.
Percentage = \( \frac { 2 }{ 3 } \times 100\% \)
Percentage = \( \frac { 200 }{ 3 } \% \)
Percentage = \( 66\frac{2}{3} \% \)
So, only \( 66\frac{2}{3} \% \) will be selected in the interview. This is a common percentage for two-thirds.
In simple words: If 2 out of 3 people are chosen, it means \( 66\frac{2}{3} \% \) will be selected.

🎯 Exam Tip: Remember common fractional to percentage conversions, like \( \frac{1}{3} = 33\frac{1}{3}\% \) and \( \frac{2}{3} = 66\frac{2}{3}\% \).

Question 3. 48 is 32% of which number?
Answer:
Let the unknown number be 'x'. We are told that 32% of x is 48. We can write this as an equation:
\( \frac { 32 }{ 100 } \times x = 48 \)
To find x, we can multiply both sides by \( \frac { 100 }{ 32 } \).
\( x = \frac { 48 \times 100 }{ 32 } \)
We can simplify the fraction. Divide 48 by 16 to get 3, and 32 by 16 to get 2.
\( x = \frac { 3 \times 100 }{ 2 } \)
\( x = \frac { 300 }{ 2 } \)
\( x = 150 \)
So, 48 is 32% of 150. This method helps us find the total amount when a percentage of it is known.
In simple words: If 32 percent of a number is 48, that number is 150. We found this by dividing 48 by 32 percent.

🎯 Exam Tip: Always set up the percentage as a fraction (e.g., 32% as \( \frac{32}{100} \)) to easily solve for the unknown quantity.

Question 4. What is 25% of 30% of 400?
Answer:
To solve this, we work step-by-step from right to left. First, we find 30% of 400.
30% of 400 = \( \frac { 30 }{ 100 } \times 400 = 30 \times 4 = 120 \)
Now, we need to find 25% of this result, which is 25% of 120.
25% of 120 = \( \frac { 25 }{ 100 } \times 120 \)
Since 25% is equal to \( \frac { 1 }{ 4 } \), we can say:
\( = \frac { 1 }{ 4 } \times 120 = 30 \)
So, 25% of 30% of 400 is 30. Breaking down percentage problems into smaller steps makes them easier to solve.
In simple words: To find 25% of 30% of 400, first find 30% of 400 (which is 120). Then, find 25% of 120, which gives 30.

🎯 Exam Tip: When dealing with "percentage of a percentage," calculate one percentage at a time, working from the innermost percentage outwards.

Question 5. If a car is sold for Rs. 2,00,000 from its original price of Rs. 3,00,000, then find the percentage of decrease in the value of the car.
Answer:
First, let's find the decrease in the car's price.
Original price = Rs. 3,00,000
Selling price = Rs. 2,00,000
Decrease in amount = Original price - Selling price
Decrease in amount = Rs. \( 3,00,000 - 2,00,000 = 1,00,000 \)
Now, to find the percentage decrease, we use the formula:
Percentage decrease = \( \frac { \text{Decrease in amount} }{ \text{Original value} } \times 100 \)
Percentage decrease = \( \frac { 1,00,000 }{ 3,00,000 } \times 100 \)
Percentage decrease = \( \frac { 1 }{ 3 } \times 100 \)
Percentage decrease = \( 33\frac{1}{3} \% \)
The car's value decreased by \( 33\frac{1}{3} \% \). Calculating percentage change is useful for understanding loss or gain.
In simple words: The car's price went down by Rs. 1,00,000. This decrease is \( 33\frac{1}{3} \% \) of its original price of Rs. 3,00,000.

🎯 Exam Tip: For percentage decrease or increase, always divide the change by the *original* value, not the new value.

Question 6. If the difference between 75% of a number and 60% of the same number is 82.5, then find 20% of that number.
Answer:
Let the unknown number be 'x'.
The difference between 75% of x and 60% of x is 82.5.
\( 75\% \text{ of } x - 60\% \text{ of } x = 82.5 \)
This can be written as:
\( \frac { 75 }{ 100 } x - \frac { 60 }{ 100 } x = 82.5 \)
\( 0.75x - 0.60x = 82.5 \)
\( 0.15x = 82.5 \)
To find x, divide 82.5 by 0.15:
\( x = \frac { 82.5 }{ 0.15 } \)
To make the division easier, multiply the numerator and denominator by 100:
\( x = \frac { 8250 }{ 15 } = 550 \)
So, the number is 550.
Now, we need to find 20% of this number (550).
20% of 550 = \( \frac { 20 }{ 100 } \times 550 \)
20% of 550 = \( \frac { 1 }{ 5 } \times 550 \)
20% of 550 = \( 110 \)
Thus, 20% of the number is 110. This problem involves multiple percentage calculations in sequence.
In simple words: We found that 15% of the number is 82.5, so the number itself is 550. Then, we calculated 20% of 550, which is 110.

🎯 Exam Tip: Break down complex percentage problems into smaller, manageable steps. First find the unknown number, then apply the next percentage calculation.

Question 7. A number when increased by 18% gives 236. Find the number.
Answer:
Let the original number be 'x'.
When the number x is increased by 18%, it means we add 18% of x to x.
\( x + 18\% \text{ of } x = 236 \)
\( x + \frac { 18 }{ 100 } x = 236 \)
To combine the terms on the left, we can write x as \( \frac { 100x }{ 100 } \).
\( \frac { 100x }{ 100 } + \frac { 18x }{ 100 } = 236 \)
\( \frac { 100x + 18x }{ 100 } = 236 \)
\( \frac { 118x }{ 100 } = 236 \)
Now, to solve for x, multiply both sides by \( \frac { 100 }{ 118 } \).
\( x = \frac { 236 \times 100 }{ 118 } \)
Since 236 is double 118 ( \( 236 \div 118 = 2 \) ):
\( x = 2 \times 100 \)
\( x = 200 \)
The original number is 200. This shows how to find the original value after a percentage increase.
In simple words: If a number plus 18% of itself equals 236, the original number is 200. We found this by setting up an equation where x plus 0.18x equals 236.

🎯 Exam Tip: A percentage increase means the new value is \( (100\% + \text{increase}\%) \) of the original number. So, \( x \times (1 + 0.18) = 236 \).

Question 8. A number when decreased by 20% gives 80. Find the number.
Answer:
Let the original number be 'x'.
When the number x is decreased by 20%, it means we subtract 20% of x from x.
\( x - 20\% \text{ of } x = 80 \)
\( x - \frac { 20 }{ 100 } x = 80 \)
To combine the terms, we can write x as \( \frac { 100x }{ 100 } \).
\( \frac { 100x }{ 100 } - \frac { 20x }{ 100 } = 80 \)
\( \frac { 80x }{ 100 } = 80 \)
Now, to solve for x, multiply both sides by \( \frac { 100 }{ 80 } \).
\( x = \frac { 80 \times 100 }{ 80 } \)
\( x = 100 \)
The original number is 100. This is how you find an original value after a percentage decrease.
In simple words: If a number minus 20% of itself is 80, the original number is 100. This means 80% of the number is 80.

🎯 Exam Tip: A percentage decrease means the new value is \( (100\% - \text{decrease}\%) \) of the original number. So, \( x \times (1 - 0.20) = 80 \).

Question 9. A number is increased by 25% and then decreased by 20%. Find the percentage change in that number.
Answer:
Let's assume the original number is 100 to make calculations easy.
First, the number is increased by 25%.
New number = Original number + 25% of Original number
New number = \( 100 + \frac { 25 }{ 100 } \times 100 = 100 + 25 = 125 \)
Next, this new number (125) is decreased by 20%.
Decrease amount = 20% of 125
Decrease amount = \( \frac { 20 }{ 100 } \times 125 = \frac { 1 }{ 5 } \times 125 = 25 \)
Final number = Number after increase - Decrease amount
Final number = \( 125 - 25 = 100 \)
Since the final number is 100, which is the same as the original number, there is no change.
Percentage change = \( \frac { \text{Final number} - \text{Original number} }{ \text{Original number} } \times 100 \)
Percentage change = \( \frac { 100 - 100 }{ 100 } \times 100 = 0\% \)
Thus, the percentage change in the number is 0%. This demonstrates that consecutive percentage changes do not always result in a net change unless calculated carefully.
In simple words: If you start with 100, increase it by 25% to get 125. Then, decrease 125 by 20% to get 100 again. So, there is no change in the number.

🎯 Exam Tip: When dealing with successive percentage changes, it's often easiest to assume an initial value (like 100) and calculate step-by-step.

Question 10. The ratio of boys and girls in a class is 5:3. If 16% of boys and 8% of girls failed in an examination, then find the percentage of passed students.
Answer:
Let the number of boys be 5k and girls be 3k, as their ratio is 5:3.
Total students = \( 5k + 3k = 8k \)
Percentage of boys who failed = 16%
Percentage of boys who passed = \( 100\% - 16\% = 84\% \)
Number of boys who passed = \( 84\% \text{ of } 5k = \frac { 84 }{ 100 } \times 5k = \frac { 420k }{ 100 } = 4.2k \)
Percentage of girls who failed = 8%
Percentage of girls who passed = \( 100\% - 8\% = 92\% \)
Number of girls who passed = \( 92\% \text{ of } 3k = \frac { 92 }{ 100 } \times 3k = \frac { 276k }{ 100 } = 2.76k \)
Total number of students who passed = Number of boys passed + Number of girls passed
Total passed = \( 4.2k + 2.76k = 6.96k \)
Now, find the overall percentage of passed students:
Percentage of passed students = \( \frac { \text{Total passed students} }{ \text{Total students} } \times 100 \)
Percentage of passed students = \( \frac { 6.96k }{ 8k } \times 100 \)
Percentage of passed students = \( \frac { 6.96 }{ 8 } \times 100 \)
Percentage of passed students = \( 0.87 \times 100 = 87\% \)
Therefore, 87% of the students passed the examination. This problem integrates ratios and percentages effectively.
In simple words: We assume there are 5 boys and 3 girls for every 'k' students. We find that 84% of boys and 92% of girls passed. Adding these up and dividing by the total students shows that 87% passed overall.

🎯 Exam Tip: When given a ratio for a total population, use a common multiplier (like 'k') for each part of the ratio to easily calculate individual group numbers.

Question 11. 12% of 250 litre is the same as _________ of 150 litre.
(A) 10%
(B) 15%
(C) 20%
(D) 30%
Answer: (C) 20%
First, calculate 12% of 250 litres:
\( 12\% \text{ of } 250 = \frac { 12 }{ 100 } \times 250 = 12 \times 2.5 = 30 \) litres.
Now, we need to find what percentage of 150 litres is 30 litres.
Percentage = \( \frac { 30 }{ 150 } \times 100\% \)
Percentage = \( \frac { 1 }{ 5 } \times 100\% = 20\% \)
So, 12% of 250 litres is the same as 20% of 150 litres. This shows how to compare quantities using percentages.
In simple words: 12% of 250 litres is 30 litres. To find what percent 30 litres is of 150 litres, we divide 30 by 150 and multiply by 100, which gives 20%.

🎯 Exam Tip: Break down the problem into two parts: calculate the actual quantity for the first percentage, then find the equivalent percentage for the second quantity.

Question 12. If three candidates A, B and C in a school election got 153,245 and 102 votes respectively, then the percentage of votes got by the winner is _____.
(A) 48%
(B) 49%
(C) 50%
(D) 45%
Answer: (B) 49%
First, find the total number of votes cast:
Total votes = Votes for A + Votes for B + Votes for C
Total votes = \( 153 + 245 + 102 = 500 \)
Next, identify the winner. The winner is the candidate with the maximum votes.
Candidate A: 153 votes
Candidate B: 245 votes (Winner)
Candidate C: 102 votes
So, the winner (Candidate B) received 245 votes.
Now, calculate the percentage of votes the winner received:
Percentage for winner = \( \frac { \text{Votes for winner} }{ \text{Total votes} } \times 100 \)
Percentage for winner = \( \frac { 245 }{ 500 } \times 100 \)
Percentage for winner = \( \frac { 245 }{ 5 } = 49\% \)
The winner received 49% of the total votes. This is a common way to analyze election results.
In simple words: The total votes are 500. The winner got 245 votes. To find the percentage, we divide 245 by 500 and multiply by 100, which is 49%.

🎯 Exam Tip: Always identify the total quantity and the specific part before calculating a percentage; for winners, it's the highest number of votes.

Question 13. 15% of 25% of 10000 = _____.
(A) 375
(B) 400
(C) 425
(D) 475
Answer: (A) 375
We need to calculate this in steps. First, find 25% of 10000.
25% of 10000 = \( \frac { 25 }{ 100 } \times 10000 = 25 \times 100 = 2500 \)
Now, find 15% of this result (2500).
15% of 2500 = \( \frac { 15 }{ 100 } \times 2500 \)
15% of 2500 = \( 15 \times 25 \)
\( 15 \times 25 = 375 \)
So, 15% of 25% of 10000 is 375. Breaking down multiple percentages into single steps makes the calculation clearer.
In simple words: First, 25% of 10000 is 2500. Then, 15% of that 2500 is 375.

🎯 Exam Tip: Always work through multiple percentage operations sequentially. Calculate the inner percentage first and use its result for the next percentage calculation.

Question 14. When 60 is subtracted from 60% of a number to give 60, the number is
(A) 60
(B) 100
(C) 150
(D) 200
Answer: (D) 200
Let the unknown number be 'x'.
The problem states that when 60 is subtracted from 60% of x, the result is 60.
So, the equation is:
\( 60\% \text{ of } x - 60 = 60 \)
\( \frac { 60 }{ 100 } x - 60 = 60 \)
Add 60 to both sides:
\( \frac { 60 }{ 100 } x = 60 + 60 \)
\( \frac { 60 }{ 100 } x = 120 \)
To find x, multiply both sides by \( \frac { 100 }{ 60 } \):
\( x = \frac { 120 \times 100 }{ 60 } \)
\( x = 2 \times 100 \)
\( x = 200 \)
The number is 200. Setting up the algebraic equation correctly is crucial here.
In simple words: If 60% of a number minus 60 gives 60, it means 60% of the number is 120. So, the number is 200.

🎯 Exam Tip: Carefully translate the word problem into a mathematical equation. "Subtracted from" means the subtraction happens *after* the initial calculation.

Question 15. If 48% of 48 = 64% of x, then x =
(A) 64
(B) 56
(C) 42
(D) 36
Answer: (D) 36
We are given the equation: \( 48\% \text{ of } 48 = 64\% \text{ of } x \)
Let's write this with fractions:
\( \frac { 48 }{ 100 } \times 48 = \frac { 64 }{ 100 } \times x \)
We can multiply both sides by 100 to remove the denominators:
\( 48 \times 48 = 64 \times x \)
To find x, divide both sides by 64:
\( x = \frac { 48 \times 48 }{ 64 } \)
We can simplify by dividing 48 and 64 by their common factor, 16.
\( 48 \div 16 = 3 \)
\( 64 \div 16 = 4 \)
So, the equation becomes:
\( x = \frac { 3 \times 48 }{ 4 } \)
Now, divide 48 by 4:
\( x = 3 \times 12 \)
\( x = 36 \)
Thus, x is 36. This problem demonstrates solving equations involving percentages.
In simple words: We set up the problem as an equation: 48% of 48 equals 64% of x. After simplifying, we found that x is 36.

🎯 Exam Tip: When an equation involves percentages on both sides, it is often helpful to convert percentages to fractions and then cancel common terms to simplify the calculation.