Percentage All Competence Aptitude

Let's assume the original price of petrol is 100 units and the original consumption by the car owner is \(x\) units, resulting in an expenditure of \(100 \times x\) units.

If the price of petrol increases by 25%, the new price becomes \(125\%\) of the original price, which is \(125\) units.

To keep the expenditure constant, the car owner needs to adjust the consumption. Let's denote the new consumption as \(y\) units.

Now, the new expenditure would be \(125 \times y\).

To avoid an increase in expenditure, we set the two expenditures equal:

\[ 100 \times x = 125 \times y \]

Now, solving for \(y\):

\[ y = \dfrac{100 \times x}{125} \]

\[ y = \dfrac{4}{5} \times x \]

This means the car owner should reduce his consumption (\(x\)) by \( \dfrac{1}{5} \times 100\% = 20\%\).

Therefore, the car owner should reduce his consumption of petrol by 20% so that the expenditure on petrol would not be increased. So, the correct answer is 20%.

Let's assume the number of boys is \(3x\) and the number of girls is \(2x\), where \(x\) is a positive constant.

Now, the total number of students in the school is \(3x + 2x = 5x\).

The number of boys who are scholarship holders is \(20\%\) of \(3x\), and the number of girls who are scholarship holders is \(25\%\) of \(2x\).

Number of boys with scholarship: \(0.20 \times 3x = 0.6x\)

Number of girls with scholarship: \(0.25 \times 2x = 0.5x\)

Total number of students with scholarship: \(0.6x + 0.5x = 1.1x\)

Now, the percentage of students with scholarships is \(\dfrac{1.1x}{5x} \times 100\).

\[\text{Percentage of students with scholarships} = \dfrac{1.1}{5} \times 100 = 22\%\]

Now, to find the percentage of students who are not scholarship holders:

\[100\% - 22\% = 78\%\]

Therefore, the percentage of the school students who are not scholarship holders is \(78\%\). So, the correct answer is 78.

Given:\[ A = \dfrac{8}{5}B \]\[ B = \dfrac{4}{5}C \]

Now, substitute the expression for B into the expression for A:

\[ A = \dfrac{8}{5} \left(\dfrac{4}{5}C\right) \]

Simplify:

\[ A = \dfrac{32}{25}C \]

So, the correct ratio of A to C is 32 : 25.

Let's use the given information to find the ratio of A to C.

1. A exceeds B by 40%: \(A = B + 0.4B\)
   Simplifying, we get \(A = 1.4B\).

2. B is less than C by 20%: \(B = C - 0.2C\)
   Simplifying, we get \(B = 0.8C\).

Now, substitute the expression for B into the expression for A:

\[A = 1.4 \times 0.8C = 1.12C\]

So, the ratio of A to C is 1.12 : 1, or simply 112 : 100.

To simplify this ratio, divide both parts by the greatest common factor, which is 4:

\[ \text{Ratio of A to C} = \dfrac{112}{4} : \dfrac{100}{4} = 28 : 25 \]

Therefore, the correct answer is 28 : 25.

Let's assume Q's salary is \(Q\). According to the given information, P's salary is 25% higher than Q's salary, which means:

\[ P = Q + 0.25Q = 1.25Q \]

Now, let's find the percentage by which Q's salary is lower than P's:

\[ \text{Percentage decrease} = \dfrac{\text{Decrease in salary}}{\text{Original salary}} \times 100 \]

\[ \text{Percentage decrease} = \dfrac{(P - Q)}{P} \times 100 \]

Substitute the expressions for P and Q:

\[ \text{Percentage decrease} = \dfrac{(1.25Q - Q)}{1.25Q} \times 100 \]

\[ \text{Percentage decrease} = \dfrac{0.25Q}{1.25Q} \times 100 = \dfrac{1}{5} \times 100 = 20\% \]

Therefore, Q's salary is 20% lower than P's salary.

So, the correct answer is 20.

Let's assume B's salary is \( B \). According to the given information, A's salary is 25% more than B's salary, which means:

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

Now, let's find the percentage by which B's salary is less than A's:

\[ \text{Percentage decrease} = \dfrac{\text{Decrease in salary}}{\text{Original salary}} \times 100 \]

\[ \text{Percentage decrease} = \dfrac{(A - B)}{A} \times 100 \]

Substitute the expressions for A and B:

\[ \text{Percentage decrease} = \dfrac{(1.25B - B)}{1.25B} \times 100 \]

\[ \text{Percentage decrease} = \dfrac{0.25B}{1.25B} \times 100 = \dfrac{1}{5} \times 100 = 20\% \]

Therefore, B's salary is 20% less than A's salary.

So, the correct answer is 20%.

Let's consider a starting number, and then apply the decrease and increase sequentially.

Let the original number be \( x \).

1. Decrease by 10%: \( x - 0.1x = 0.9x \)
2. Increase by 10%: \( 0.9x + 0.1(0.9x) = 0.99x \)

Now, let's find the percentage change:

\[ \text{Percentage Change} = \dfrac{\text{Final Value} - \text{Initial Value}}{\text{Initial Value}} \times 100 \]

\[ \text{Percentage Change} = \dfrac{(0.99x - x)}{x} \times 100 = -0.01 \times 100 = -1\% \]

So, the percentage change is a decrease of 1%.

Therefore, the correct answer is 1% decrease.

Let's use algebraic representation to solve the problem:

1. A is equal to 20% of B: \( A = 0.2B \)
2. B is equal to 25% of C: \( B = 0.25C \)

Now, substitute the expression for B into the expression for A:

\[ A = 0.2 \times (0.25C) \]

Simplify:

\[ A = 0.05C \]

Now, we want to find the percentage of C that is equal to A:

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

Substitute the expression for A:

\[ \text{Percentage} = \dfrac{0.05C}{C} \times 100 = 0.05 \times 100 = 5\% \]

Therefore, 5% of C is equal to A.

So, the correct answer is 5.

If A earns 25% more than B, it means A's salary is 125% of B's salary. 

\[ A = 1.25B \]

Now, let's find the percentage by which B earns less than A:

\[ \text{Percentage decrease} = \dfrac{\text{Decrease in salary}}{\text{Original salary}} \times 100 \]

\[ \text{Percentage decrease} = \dfrac{(A - B)}{A} \times 100 \]

Substitute the expressions for A and B:

\[ \text{Percentage decrease} = \dfrac{(1.25B - B)}{1.25B} \times 100 \]

\[ \text{Percentage decrease} = \dfrac{0.25B}{1.25B} \times 100 = \dfrac{1}{5} \times 100 = 20\% \]

Therefore, B earns 20% less than A.

So, the correct answer is 20%.

Let the whole number be represented by \( x \).

Given that 51% of \( x \) is 714:

\[ 0.51x = 714 \]

Now, solve for \( x \):

\[ x = \dfrac{714}{0.51} \]

\[ x \approx 1400 \]

Now, find 25% of that number:

\[ 0.25 \times 1400 = 350 \]

Therefore, 25% of the whole number is 350.

So, the correct answer is 350.