Percentage All Competence Aptitude

Let's denote the unknown number as \( x \).

We are given that 18% of \( x \) is equal to 12% of 75:

\[ 0.18x = 0.12 \times 75 \]

Now, solve for \( x \):

\[ 0.18x = 9 \]

\[ x = \dfrac{9}{0.18} \]

\[ x = 50 \]

Therefore, the unknown number is 50.

So, the correct answer is 50.

Let's break down the given information and set up the equations:

1. \(50\% \text{ of } (P - Q) = 30\% \text{ of } (P + Q)\)

\[0.5(P - Q) = 0.3(P + Q)\]

2. \(Q = x\% \text{ of } P\)

\[Q = \dfrac{x}{100}P\]

Now, let's work with the first equation:

\[0.5(P - Q) = 0.3(P + Q)\]

Distribute the percentages:

\[0.5P - 0.5Q = 0.3P + 0.3Q\]

Combine like terms:

\[0.2P = 0.8Q\]

Now, let's use the second equation:

\[Q = \dfrac{x}{100}P\]

Substitute this into the equation we derived:

\[0.2P = 0.8 \left(\dfrac{x}{100}P\right)\]

Simplify:

\[0.2P = \dfrac{8x}{100}P\]

Multiply both sides by 100 to get rid of the fraction:

\[20P = 8xP\]

Divide both sides by \(8P\):

\[x = \dfrac{20}{8} = 2.5\]

So, the value of \(x\) is 2.5, which corresponds to 25%.

Therefore, the correct answer is 25.

Let's set up the equation using the given information:

\[ 15\% \text{ of } (A + B) = 25\% \text{ of } (A - B) \]

This can be written as:

\[ 0.15(A + B) = 0.25(A - B) \]

Now, let's solve for the relationship between A and B:

\[ 0.15A + 0.15B = 0.25A - 0.25B \]

Combine like terms:

\[ 0.15B + 0.25B = 0.25A - 0.15A \]

\[ 0.40B = 0.10A \]

Divide both sides by 0.10A to isolate B:

\[ B = \dfrac{0.10A}{0.40} \]

Simplify:

\[ B = \dfrac{1}{4}A \]

Now, let's find what percent of B is equal to A:

\[ \text{Percentage} = \dfrac{A}{B} \times 100 \]

Substitute the expression for B:

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

\[ \text{Percentage} = \dfrac{4}{1} \times 100 = 400\% \]

Therefore, what percent of B is equal to A is 400%.

So, the correct answer is 400%.

To find what percent 72 grams is of 3.6 kg, you can use the formula:

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

In this case, the part is 72 grams and the whole is 3.6 kg (which is equivalent to 3600 grams).

\[ \text{Percentage} = \left( \dfrac{72}{3600} \right) \times 100 \]

Simplify the fraction:

\[ \text{Percentage} = \left( \dfrac{1}{50} \right) \times 100 \]

\[ \text{Percentage} = 2\% \]

Therefore, 72 grams is 2% of 3.6 kg.

So, the correct answer is 2%.

Let's set up the equation based on the given information:

Let \( x \) be the value to be added to 15% of 160.

The sum of \( x \) and 15% of 160 should be equal to 25% of 240:

\[ x + 0.15(160) = 0.25(240) \]

Now, solve for \( x \):

\[ x + 24 = 60 \]

Subtract 24 from both sides:

\[ x = 60 - 24 \]

\[ x = 36 \]

Therefore, to make the sum equal to 25% of 240, you need to add 36.

So, the correct answer is 36.

Let's calculate the discounted price for a dozen pairs of socks.

Original price for a dozen pairs of socks = 180

Discount rate = 20%

Discount amount = 20% of 180 = 0.20 * 180 = 36

Discounted price = Original price - Discount amount = 180 - 36 = 144

Now, let's find the cost per pair after the discount:

Cost per pair = Discounted price / Number of pairs = 144 / 12 = 12

So, each pair costs 12.

Now, let's see how many pairs can be bought for 48:

Number of pairs = Total amount / Cost per pair = 48 / 12 = 4

Therefore, 4 pairs of socks can be bought for 48. 

So, the correct answer is 4 pairs.

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

\[ 60\% \text{ of } x - 60 = 60 \]

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

\[ 0.6x - 60 = 60 \]

Add 60 to both sides:

\[ 0.6x = 120 \]

Divide both sides by 0.6:

\[ x = \dfrac{120}{0.6} \]

\[ x = 200 \]

So, the number is 200.

Therefore, the correct answer is 200.

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

\[ 75 + 75\% \text{ of } x = x \]

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

\[ 75 + 0.75x = x \]

Subtract 0.75x from both sides:

\[ 75 = 0.25x \]

Divide both sides by 0.25:

\[ x = \dfrac{75}{0.25} \]

\[ x = 300 \]

Now, find 40% of that number:

\[ 0.40 \times 300 = 120 \]

Therefore, 40% of the number is 120.

So, the correct answer is 120.

Let's break down the given information and set up the equation:

\[ x\% \text{ of } y\% \text{ of } 80 = 25\% \text{ of } 900 \]

Translate this into an equation:

\[ \left(\dfrac{x}{100} \times \dfrac{y}{100} \times 80\right) = \dfrac{25}{100} \times 900 \]

Simplify both sides:

\[ \dfrac{xy}{125} \times 80 = \dfrac{225}{4} \]

Multiply both sides by \( \dfrac{125}{80} \) to solve for \( xy \):

\[ xy = \dfrac{225}{4} \times \dfrac{125}{80} \times 80 \]

\[ xy = \dfrac{225}{4} \times 125 \]

\[ xy = \dfrac{28125}{4} \]

So, the value of \( xy \) is \( \dfrac{28125}{4} \).

The closest option is 28125.

Therefore, the correct answer is 28125.

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

\[ 50\% \text{ of } x + 50 = x \]

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

\[ 0.5x + 50 = x \]

Subtract \( 0.5x \) from both sides:

\[ 50 = 0.5x \]

Divide both sides by 0.5:

\[ x = \dfrac{50}{0.5} \]

\[ x = 100 \]

So, the number is 100.

Therefore, the correct answer is 100.