Exercise : Percentage - General Questions
✔ Percentage -
General Questions
21.
The value of a machine depreciates at 10% per annum. If its present value is $162,000, what was its value 2 years ago?
View Answer
Answer: Option B
Explanation:
Explanation:
1. Let the value 2 years ago be \(X\).
2. After 1st year depreciation: \(X \times 0.9\).
3. After 2nd year depreciation: \(X \times 0.9 \times 0.9 = 162,000\).
4. \(X \times 0.81 = 162,000\).
5. \(X = \frac{162,000}{0.81} = 200,000\).
2. After 1st year depreciation: \(X \times 0.9\).
3. After 2nd year depreciation: \(X \times 0.9 \times 0.9 = 162,000\).
4. \(X \times 0.81 = 162,000\).
5. \(X = \frac{162,000}{0.81} = 200,000\).
22.
If 60% of A's income is equal to 75% of B's income, then B's income is equal to x% of A's income. Find x.
View Answer
Answer: Option C
Explanation:
Explanation:
1. Write the equation: \(0.60A = 0.75B\).
2. Solve for B in terms of A: \(B = \frac{0.60}{0.75}A\).
3. Simplify the fraction: \(\frac{60}{75} = \frac{4}{5} = 0.8\).
4. \(B = 0.8A\).
5. Convert 0.8 to percentage: \(0.8 \times 100 = 80\%\).
6. Therefore, \(x = 80\).
2. Solve for B in terms of A: \(B = \frac{0.60}{0.75}A\).
3. Simplify the fraction: \(\frac{60}{75} = \frac{4}{5} = 0.8\).
4. \(B = 0.8A\).
5. Convert 0.8 to percentage: \(0.8 \times 100 = 80\%\).
6. Therefore, \(x = 80\).
23.
In a class, 60% of students are boys and the rest are girls. If 20% of boys and 25% of girls are scholarship holders, find the % of students who do NOT have a scholarship.
View Answer
Answer: Option C
Explanation:
Explanation:
1. Let total students = 100. Then Boys = 60 and Girls = 40.
2. Boys without scholarship: \(80\% \text{ of } 60 = 48\).
3. Girls without scholarship: \(75\% \text{ of } 40 = 30\).
4. Total students without scholarship: \(48 + 30 = 78\).
5. Since total students = 100, the percentage is 78%.
2. Boys without scholarship: \(80\% \text{ of } 60 = 48\).
3. Girls without scholarship: \(75\% \text{ of } 40 = 30\).
4. Total students without scholarship: \(48 + 30 = 78\).
5. Since total students = 100, the percentage is 78%.
24.
A's weight is 20% more than B's, whose weight is 30% more than C's. By how much percent is A's weight more than C's?
View Answer
Answer: Option B
Explanation:
Explanation:
1. Let weight of C = 100.
2. B's weight = \(100 + 30\% = 130\).
3. A's weight = \(130 + 20\% \text{ of } 130 = 130 + 26 = 156\).
4. Difference between A and C = \(156 - 100 = 56\).
5. Percentage difference = 56%.
2. B's weight = \(100 + 30\% = 130\).
3. A's weight = \(130 + 20\% \text{ of } 130 = 130 + 26 = 156\).
4. Difference between A and C = \(156 - 100 = 56\).
5. Percentage difference = 56%.
25.
Due to a reduction of 20% in the price of wheat, a man can buy 5 kg more for $320. Find the original price per kg.
View Answer
Answer: Option C
Explanation:
Explanation:
1. Savings due to reduction: \(20\% \text{ of } 320 = 64\).
2. With this $64, the man buys 5 kg extra. So, current price = \(64 / 5 = 12.80\) per kg.
3. This current price is 80% of the original price (since it was reduced by 20%).
4. Original Price \(\times 0.8 = 12.80\).
5. Original Price = \(12.80 / 0.8 = 16\).
2. With this $64, the man buys 5 kg extra. So, current price = \(64 / 5 = 12.80\) per kg.
3. This current price is 80% of the original price (since it was reduced by 20%).
4. Original Price \(\times 0.8 = 12.80\).
5. Original Price = \(12.80 / 0.8 = 16\).
26.
If x is 80% of y, what percent of x is y?
View Answer
Answer: Option B
Explanation:
Explanation:
1. Write the relation: \(x = 0.8y\).
2. Rearrange to find \(y\) in terms of \(x\): \(y = \frac{x}{0.8}\).
3. To find what percent \(y\) is of \(x\), calculate \(\left( \frac{y}{x} \right) \times 100\).
4. \(\left( \frac{1}{0.8} \right) \times 100 = 1.25 \times 100 = 125\%\).
2. Rearrange to find \(y\) in terms of \(x\): \(y = \frac{x}{0.8}\).
3. To find what percent \(y\) is of \(x\), calculate \(\left( \frac{y}{x} \right) \times 100\).
4. \(\left( \frac{1}{0.8} \right) \times 100 = 1.25 \times 100 = 125\%\).
27.
A student has to obtain 33% of total marks to pass. He got 125 marks and failed by 40 marks. Find the total marks.
View Answer
Answer: Option B
Explanation:
Explanation:
1. Calculate passing marks: \(125 + 40 = 165\).
2. According to the problem, \(33\% \text{ of Total Marks} = 165\).
3. Let Total Marks be \(T\). \(0.33T = 165\).
4. \(T = \frac{165}{0.33} = 500\).
2. According to the problem, \(33\% \text{ of Total Marks} = 165\).
3. Let Total Marks be \(T\). \(0.33T = 165\).
4. \(T = \frac{165}{0.33} = 500\).
28.
If the numerator of a fraction is increased by 200% and denominator by 350%, the resultant fraction is 5/12. Find the original fraction.
View Answer
Answer: Option B
Explanation:
Explanation:
1. Let original fraction be \(x/y\).
2. New numerator: \(x + 200\% \text{ of } x = 300\% \text{ of } x\).
3. New denominator: \(y + 350\% \text{ of } y = 450\% \text{ of } y\).
4. Equation: \(\frac{300x}{450y} = \frac{5}{12}\).
5. Simplify ratio: \(\frac{300}{450} = \frac{2}{3}\).
6. \(\frac{2x}{3y} = \frac{5}{12} \implies \frac{x}{y} = \frac{5}{12} \times \frac{3}{2} = \frac{15}{24} = \frac{5}{8}\).
2. New numerator: \(x + 200\% \text{ of } x = 300\% \text{ of } x\).
3. New denominator: \(y + 350\% \text{ of } y = 450\% \text{ of } y\).
4. Equation: \(\frac{300x}{450y} = \frac{5}{12}\).
5. Simplify ratio: \(\frac{300}{450} = \frac{2}{3}\).
6. \(\frac{2x}{3y} = \frac{5}{12} \implies \frac{x}{y} = \frac{5}{12} \times \frac{3}{2} = \frac{15}{24} = \frac{5}{8}\).
29.
Two numbers are less than a third number by 30% and 37% respectively. By how much percent is the second number less than the first?
View Answer
Answer: Option B
Explanation:
Explanation:
1. Let the 3rd number be 100.
2. 1st number = \(100 - 30 = 70\).
3. 2nd number = \(100 - 37 = 63\).
4. Difference between 1st and 2nd = \(70 - 63 = 7\).
5. Percentage 2nd is less than 1st: \(\left( \frac{7}{70} \right) \times 100 = 10\%\).
2. 1st number = \(100 - 30 = 70\).
3. 2nd number = \(100 - 37 = 63\).
4. Difference between 1st and 2nd = \(70 - 63 = 7\).
5. Percentage 2nd is less than 1st: \(\left( \frac{7}{70} \right) \times 100 = 10\%\).
30.
In an office, 40% of staff are female. 40% of females and 60% of males voted for me. What percentage of total votes did I get?
View Answer
Answer: Option B
Explanation:
Explanation:
1. Let total staff = 100. Female = 40, Male = 60.
2. Female votes: \(40\% \text{ of } 40 = 16\).
3. Male votes: \(60\% \text{ of } 60 = 36\).
4. Total votes: \(16 + 36 = 52\).
5. Percentage of total: 52%.
2. Female votes: \(40\% \text{ of } 40 = 16\).
3. Male votes: \(60\% \text{ of } 60 = 36\).
4. Total votes: \(16 + 36 = 52\).
5. Percentage of total: 52%.