Percentage objective type question set 2

Answer: b. 50

Explanation:
Let the required number be \( x \).
According to the question:
18% of \( x \) = 12% of 75

\[ \frac{18}{100} \times x = \frac{12}{100} \times 75 \]
\[ 18 \times x = 12 \times 75 \]
\[ x = \frac{12 \times 75}{18} \]

Simplifying the fraction:
\[ x = \frac{2 \times 75}{3} \]
\[ x = 2 \times 25 \]
x = 50

Answer: b. 20%

Explanation:
Let the Marked Price (MP) of one article be \( x \).
Total articles received by the customer = \( 4 + 1 = 5 \).

Total Marked Price of 5 articles = \( 5x \)
Total Selling Price (price of 4 articles) = \( 4x \)

Discount = Total MP \( – \) Total SP
Discount = \( 5x – 4x = x \)

Discount Percentage:
\[ \text{Discount } \% = \left( \frac{\text{Discount}}{\text{Total Marked Price}} \right) \times 100 \]
\[ \text{Discount } \% = \left( \frac{x}{5x} \right) \times 100 \]
\[ \text{Discount } \% = \frac{100}{5} = 20\% \]
The effective discount is 20%.

Answer: b. 280

Explanation:
Let the required number be \( x \).
According to the question, 52% of the number is 728.

Step 1: Find the number (\( x \))
\[ x \times \frac{52}{100} = 728 \]
\[ x = \frac{728 \times 100}{52} \]
\[ x = 14 \times 100 = 1400 \]

Step 2: Find 20% of that number
\[ 20\% \text{ of } 1400 = 1400 \times \frac{20}{100} \]
\[ = 14 \times 20 \]
\[ = 280 \]
The final result is 280.

Answer: d. 3 litre

Solution:
The amount of substance (or solute) in the solution can be calculated as follows:

\[ 15 \times \frac{20}{100} = 3 \text{ litres} \]
The final volume is 3 litres.

Answer: b. 32

Answer: a. 26,620

Explanation:
Current population = 20,000
Rate of increase = 10% per annum
Time = 3 years

The population after 3 years can be calculated using the compound growth formula:
\[ \text{New Population} = \text{Present Population} \times \left(1 + \frac{r}{100}\right)^n \]
\[ = 20000 \times \frac{110}{100} \times \frac{110}{100} \times \frac{110}{100} \]
\[ = 20000 \times \frac{11}{10} \times \frac{11}{10} \times \frac{11}{10} \]
\[ = 20 \times 11 \times 11 \times 11 \]
\[ = 20 \times 1331 \]
\[ = 26620 \]
The population of the town after 3 years will be 26,620.

Answer: d. 14,641

Explanation:
Initial Salary = 10,000
Monthly Increase = 10%
Time period (January to May) = 4 months

The salary after 4 months can be calculated as:
\[ \text{Final Salary} = 10000 \times \left(\frac{110}{100}\right)^4 \]
\[ = 10000 \times \frac{11}{10} \times \frac{11}{10} \times \frac{11}{10} \times \frac{11}{10} \]
\[ = 10000 \times \frac{14641}{10000} \]
\[ = 14641 \]
The salary of the employee in May will be 14,641.

Answer: b. 5,600

Explanation:
Let the number of males be \( x \).
Then, the number of females = \( 9800 – x \).

Step 1: Set up the equation based on growth
Increase in males is 8% and females is 5%. The new total population is 10458.
\[ x \times \frac{108}{100} + (9800 – x) \times \frac{105}{100} = 10458 \]

Step 2: Simplify and solve for \( x \)
Multiply the entire equation by 100 to remove denominators:
\[ 108x + 105(9800 – x) = 1045800 \]
\[ 108x + 1029000 – 105x = 1045800 \]
\[ 3x = 1045800 – 1029000 \]
\[ 3x = 16800 \]
\[ x = \frac{16800}{3} = 5600 \]
The number of males in the town was 5,600.

Answer: b. 0.1%

Solution:
To convert a percentage to a decimal, divide the value by 100.

\[ 0.1\% = \frac{0.1}{100} = 0.001 \]
The decimal value is 0.001.

Answer: a. 150

Explanation:
Let the number be \( x \).
According to the question, when 60 is added to 60% of \( x \), the result is the number itself (\( x \)).

Equation:
\[ 60\% \text{ of } x + 60 = x \]
\[ \frac{60}{100} \times x + 60 = x \]
\[ \frac{3x}{5} + 60 = x \]

Solving for \( x \):
\[ x – \frac{3x}{5} = 60 \]
\[ \frac{5x – 3x}{5} = 60 \]
\[ \frac{2x}{5} = 60 \]
\[ 2x = 300 \]
\[ x = 150 \]
The required number is 150.

Answer: b. 60

Explanation:
Let the number be \( x \).
According to the question, when 50 is added to 50% of \( x \), the result is the number itself (\( x \)).

Step 1: Find the number (\( x \))
\[ 50\% \text{ of } x + 50 = x \]
\[ \frac{50}{100} \times x + 50 = x \]
\[ \frac{x}{2} + 50 = x \]
\[ x – \frac{x}{2} = 50 \]
\[ \frac{x}{2} = 50 \]
\[ x = 100 \]

Step 2: Find 60% of the number
Now, we need to find 60% of 100:
\[ 60\% \text{ of } 100 = \frac{60}{100} \times 100 = 60 \]
The final answer is 60.

Answer: d. 40%

Explanation:
Let the third number be 100.
According to the question:
First number = 20% of 100 = 20
Second number = 50% of 100 = 50

To find: What percent of the second number is the first number?
Let the required percentage be \( x\% \).
\[ 50 \times \frac{x}{100} = 20 \]
\[ \frac{x}{2} = 20 \]
\[ x = 40 \]
The first number is 40% of the second number.

Answer: c. 90%

Explanation:
Let the third number be 100.
According to the question:
First number = 72% of 100 = 72
Second number = 80% of 100 = 80

To find: What percent of the second number is the first number?
Let the required percentage be \( x\% \).
\[ 80 \times \frac{x}{100} = 72 \]
\[ \frac{4x}{5} = 72 \]
\[ x = \frac{72 \times 5}{4} \]
\[ x = 18 \times 5 = 90 \]
The first number is 90% of the second number.

Answer: c. 90%

Explanation:
Let the number to be added be \( x \).
According to the question:
10% of 320 + \( x \) = 30% of 230

Step 1: Calculate the percentages
\[ \left( \frac{10}{100} \times 320 \right) + x = \left( \frac{30}{100} \times 230 \right) \]
\[ 32 + x = 69 \]

Step 2: Solve for \( x \)
\[ x = 69 – 32 \]
\[ x = 37 \]
The number to be added is 37.

Answer: c. Rs 30,000

Explanation:
Let the total sales be \( x \).
According to the question:
– 5% commission on the first 10,000
– 6% commission on sales exceeding 10,000
Total commission earned = 1,700

Step 1: Set up the equation
\[ \left( 10000 \times \frac{5}{100} \right) + \left( (x – 10000) \times \frac{6}{100} \right) = 1700 \]

Step 2: Simplify and solve for \( x \)
\[ 500 + \frac{6(x – 10000)}{100} = 1700 \]
\[ \frac{6(x – 10000)}{100} = 1700 – 500 \]
\[ \frac{6(x – 10000)}{100} = 1200 \]
\[ 6(x – 10000) = 120000 \]
\[ x – 10000 = 20000 \]
\[ x = 30000 \]
The total sales made by the salesman are 30,000.

Answer: b. 20%

Explanation:
Let the income of B be 100.
Since A’s income is 25% more than B’s, then:
Income of A = 125.

To find: By what percent is B’s income less than A’s?
Difference in income = \( 125 – 100 = 25 \).

We need to find what percent 25 is of A’s income (125):
\[ \text{Percentage Less} = \left( \frac{\text{Difference}}{\text{A’s Income}} \right) \times 100 \]
\[ = \frac{25}{125} \times 100 \]
\[ = \frac{1}{5} \times 100 \]
\[ = 20\% \]
B’s income is 20% less than A’s income.

Answer: d. 2.5%

Explanation:
First, we need to find the total number of minutes in a full day (24 hours).
Total minutes = \( 24 \text{ hours} \times 60 \text{ minutes} = 1440 \text{ minutes} \).

To find: What percent of 1440 minutes is 36 minutes?
\[ \text{Percentage} = \left( \frac{36}{24 \times 60} \right) \times 100 \]
\[ = \frac{36}{1440} \times 100 \]
\[ = \frac{1}{40} \times 100 \]
\[ = 2.5\% \]
36 minutes is 2.5% of a day.

Answer: b. 0.25%

Explanation:
The question asks for 1% of 1% of 25% of 1000. We convert each percentage into a fraction with a denominator of 100.

Step-by-Step Calculation:
\[ = \frac{1}{100} \times \frac{1}{100} \times \frac{25}{100} \times 1000 \]
\[ = \frac{1 \times 1 \times 25 \times 1000}{100 \times 100 \times 100} \]
\[ = \frac{25000}{1000000} \]
\[ = \frac{25}{100} = 0.25 \]
The final value is 0.25.

Answer: a. 48

Explanation:
To find the number that is 40% less than 80, we follow these steps:

Step 1: Calculate 40% of 80
\[ \text{Value} = \frac{40}{100} \times 80 = 32 \]

Step 2: Subtract this value from the original number
\[ \text{Result} = 80 – 32 = 48 \]
The number which is 40% less than 80 is 48.

Answer: b. 4% decrease

Answer: b. 4% decrease
Explanation:
Let the initial number be 100.

Step 1: Apply 20% increase
New Number = \( 100 + 20\% \text{ of } 100 = 120 \)

Step 2: Apply 20% decrease on the new number
Final Number = \( 120 – 20\% \text{ of } 120 \)
\[ 100 \times \frac{120}{100} \times \frac{80}{100} = 96 \]

Step 3: Calculate the net change
Net Change = \( 96 – 100 = -4 \)
A change of -4 on a base of 100 is a 4% decrease.