Percentage All Competence Aptitude

To find what percentage of a day is 30 minutes, you can use the following formula:

\[ \text{Percentage} = \left( \dfrac{\text{Part}}{\text{Whole}} \right) \times 100 \]

Here, the part is 30 minutes, and the whole is the total minutes in a day, which is 24 hours \(\times\) 60 minutes = 1440 minutes.

\[ \text{Percentage} = \left( \dfrac{30}{1440} \right) \times 100 \]

Simplify the fraction:

\[ \text{Percentage} = \left( \dfrac{1}{48} \right) \times 100 \]

\[ \text{Percentage} \approx 2.083\% \]

So, the correct answer is 2.083.

The "Buy 4 Get 1 Free" offer essentially means that for every 4 items you buy, you get 1 item free. In terms of a percentage discount, you are essentially paying for only 4 items when you get 5 items. 

Let's calculate the effective discount percentage:

\[ \text{Effective Discount Percentage} = \left( \dfrac{\text{Number of items bought} - \text{Number of free items}}{\text{Number of items bought}} \right) \times 100 \]

In this case, the effective discount percentage is:

\[ \text{Effective Discount Percentage} = \left( \dfrac{4}{5} \right) \times 100 = 80\% \]

So, the net percentage of discount is 80%. 

Therefore, the closest option is 20%.

So, the correct answer is 20%.

Let's denote the initial number of students as \(x\). According to the given information:

\[ x + 20\% \text{ of } x = 66 \]

Translate this into an equation and solve for \(x\):

\[ x + 0.20x = 66 \]

Combine like terms:

\[ 1.20x = 66 \]

Divide both sides by 1.20 to solve for \(x\):

\[ x = \dfrac{66}{1.20} \]

\[ x = 55 \]

So, the initial number of students was 55.

Therefore, the correct answer is 55.

Let's denote the total number of people in the marriage party as \( T \).

The percentage of women is 32%, and the percentage of men is 54%. The remaining percentage is for children.

The percentage of children is given by:\[ \text{Percentage of children} = 100\% - \text{Percentage of women} - \text{Percentage of men} \]\[ \text{Percentage of children} = 100\% - 32\% - 54\% = 14\% \]

Now, we know that 14% of the total number represents 196 children.

Let \( C \) be the total number of children. We can set up the equation:\[ 0.14 \times T = 196 \]

Solve for \( T \):\[ T = \dfrac{196}{0.14} \]

\[ T = 1400 \]

Now, we can find the number of men (54% of the total):\[ \text{Number of men} = 0.54 \times 1400 \]

\[ \text{Number of men} = 756 \]

So, there are 756 men in the marriage party.

Therefore, the correct answer is 756.

Let's assume B's income is \( x \).

According to the given information, A's income is 25% more than B's income:

\[ A = x + 0.25x = 1.25x \]

Now, we want to find what percent of A's income is B's income:

\[ \text{Percentage} = \left( \dfrac{\text{B's income}}{\text{A's income}} \right) \times 100 \]

Substitute the values:

\[ \text{Percentage} = \left( \dfrac{x}{1.25x} \right) \times 100 \]

Cancel out the common factor of \( x \):

\[ \text{Percentage} = \left( \dfrac{1}{1.25} \right) \times 100 \]

\[ \text{Percentage} = \dfrac{4}{5} \times 100 \]

\[ \text{Percentage} = 80\% \]

Therefore, B's income is 80% of A's income.

So, the correct answer is 80.

If \( x \) is 5 times longer than \( y \), it means:

\[ x = 5y \]

Now, let's find the percentage by which \( y \) is less than \( x \):

\[ \text{Percentage less than } x = \left( \dfrac{x - y}{x} \right) \times 100 \]

Substitute the expression for \( x \):

\[ \text{Percentage less than } x = \left( \dfrac{5y - y}{5y} \right) \times 100 \]

Simplify the expression:

\[ \text{Percentage less than } x = \left( \dfrac{4y}{5y} \right) \times 100 \]

Cancel out the common factor of \( y \):

\[ \text{Percentage less than } x = \left( \dfrac{4}{5} \right) \times 100 \]

\[ \text{Percentage less than } x = 80\% \]

Therefore, \( y \) is 80% less than \( x \).

So, the correct answer is 80%.

Let's assume B's income is \( x \).

According to the given information, A's income is 40% less than that of B:

\[ A = x - 0.40x = 0.60x \]

Now, we want to find how much percent B's income is more than that of A:

\[ \text{Percentage more than } A = \left( \dfrac{x - 0.60x}{0.60x} \right) \times 100 \]

Simplify the expression:

\[ \text{Percentage more than } A = \left( \dfrac{0.40x}{0.60x} \right) \times 100 \]

Cancel out the common factor of \( x \):

\[ \text{Percentage more than } A = \left( \dfrac{2}{3} \right) \times 100 \]

\[ \text{Percentage more than } A = 66.66\% \]

Therefore, B's income is 66.66% more than that of A.

So, the correct answer is 66.66%.

Let's denote the person's income as \(x\).

1. The person gave 20% of his income to his elder son, which means he is left with \(0.8x\) after this donation.
2. Then, he gave 30% of the remaining to his younger son, leaving him with \(0.7 \times 0.8x\) after this donation.
3. Finally, he donated 10% of the remaining balance to a trust, leaving him with \(0.9 \times 0.7 \times 0.8x\).

According to the given information, he is left with $10,080:

\[ 0.9 \times 0.7 \times 0.8x = 10,080 \]

Now, solve for \(x\):

\[ x = \dfrac{10,080}{0.9 \times 0.7 \times 0.8} \]

\[ x = \dfrac{10,080}{0.504} \]

\[ x = 20,000 \]

Therefore, the person's income was $20,000.

Let's assume the original wages were \(x\).

After a 20% cut, the worker's new wages are \(0.8x\) (80% of the original).

Now, to regain the original wages, the worker needs to obtain a rise of:

\[ \text{Rise} = \dfrac{\text{Original Wages} - \text{New Wages}}{\text{New Wages}} \times 100 \]

\[ \text{Rise} = \dfrac{x - 0.8x}{0.8x} \times 100 \]

\[ \text{Rise} = \dfrac{0.2x}{0.8x} \times 100 \]

\[ \text{Rise} = \dfrac{1}{4} \times 100 \]

\[ \text{Rise} = 25\% \]

Therefore, the worker needs to obtain a rise of 25% to regain his original wages. 

So, the correct answer is 25.0%.

Let's denote Kashyap's salary as \(x\).

According to the given information, Tulsiram's salary is 20% more than that of Kashyap:

\[ \text{Tulsiram's salary} = x + 0.20x = 1.20x \]

Now, Tulsiram saves 720, which is 4% of his salary:

\[ 0.04 \times \text{Tulsiram's salary} = 720 \]

Substitute the expression for Tulsiram's salary:

\[ 0.04 \times 1.20x = 720 \]

Solve for \(x\):

\[ 0.048x = 720 \]

\[ x = \dfrac{720}{0.048} \]

\[ x = 15,000 \]

Therefore, Kashyap's salary is 15,000.

So, the correct answer is 15,000.