Percentage All Competence Aptitude

Let's denote the original price of the book as \( P \).

First, the price is decreased by 25%, which means the new price (\( P_1 \)) is given by:\[ P_1 = P - 0.25P = 0.75P \]

Then, the resulting price is increased by 20%, which means the final price (\( P_2 \)) is given by:\[ P_2 = P_1 + 0.20P_1 = 1.20 \times 0.75P = 0.90P \]

Now, let's calculate the net change:\[ \text{Net Change} = \dfrac{P_2 - P}{P} \times 100 \]

Substitute the values:\[ \text{Net Change} = \dfrac{0.90P - P}{P} \times 100 \]

Simplify the expression:\[ \text{Net Change} = \dfrac{-0.10P}{P} \times 100 \]

Cancel out \(P\) from the numerator and denominator:\[ \text{Net Change} = -0.10 \times 100 \]

\[ \text{Net Change} = -10\% \]

Therefore, the net change in the price of the book is a 10% decrease. Hence, the correct answer is a 10% decrease.

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

First, the number is increased by 20%, which means the new number (\(x_1\)) is given by:\[ x_1 = x + 0.20x = 1.20x \]

Then, the resulting number is decreased by 10%, which means the final number (\(x_2\)) is given by:\[ x_2 = x_1 - 0.10x_1 = 0.90 \times 1.20x = 1.08x \]

Now, let's calculate the net change:\[ \text{Net Change} = \dfrac{x_2 - x}{x} \times 100 \]

Substitute the values:\[ \text{Net Change} = \dfrac{1.08x - x}{x} \times 100 \]

Simplify the expression:\[ \text{Net Change} = \dfrac{0.08x}{x} \times 100 \]

Cancel out \(x\) from the numerator and denominator:\[ \text{Net Change} = 0.08 \times 100 \]

\[ \text{Net Change} = 8\% \]

Therefore, the net change in the number is an 8% increase. Hence, the correct answer is an 8% increase.

Let's denote the total number of votes recorded as \(T\).

The candidate secured 40% of the votes, which means the number of votes received by the candidate (\(V_1\)) is given by:\[ V_1 = 0.40T \]

The other candidate defeated the first candidate by a majority of 298 votes. Therefore, the votes received by the other candidate (\(V_2\)) is:\[ V_2 = V_1 + 298 \]

Now, we can set up an equation using the percentages and the total number of votes:\[ V_1 + V_2 = T \]

Substitute the expressions for \(V_1\) and \(V_2\):\[ 0.40T + (0.40T + 298) = T \]

Combine like terms:\[ 0.80T + 298 = T \]

Subtract \(0.80T\) from both sides:\[ 298 = 0.20T \]

Now, solve for \(T\):\[ T = \dfrac{298}{0.20} \]

\[ T = 1490 \]

Therefore, the total number of votes recorded is 1490. Hence, the correct answer is 1490.

Let's denote the total number of votes polled as \(T\).

The candidate who won got 60% of the votes, which means the number of votes received by the winning candidate (\(V_1\)) is given by:\[ V_1 = 0.60T \]

The winning margin is given as 1600 votes, so the votes received by the other candidate (\(V_2\)) is:\[ V_2 = V_1 - 1600 \]

Now, we can set up an equation using the percentages and the total number of votes:\[ V_1 + V_2 = T \]

Substitute the expressions for \(V_1\) and \(V_2\):\[ 0.60T + (0.60T - 1600) = T \]

Combine like terms:\[ 1.20T - 1600 = T \]

Subtract \(T\) from both sides:\[ 0.20T = 1600 \]

Now, solve for \(T\):\[ T = \dfrac{1600}{0.20} \]

\[ T = 8000 \]

Therefore, the total number of votes polled is 8000. Hence, the correct answer is 8000.

Let's denote the total number of votes polled as \(T\).

The candidate who got 84% of the votes (let's call it \(V_1\)) received \(0.84T\) votes.

The majority is given as 476 votes, so the votes received by the other candidate (\(V_2\)) is \(V_1 - 476\).

Now, we can set up an equation using the percentages and the total number of votes:\[ V_1 + V_2 = T \]

Substitute the expressions for \(V_1\) and \(V_2\):\[ 0.84T + (0.84T - 476) = T \]

Combine like terms:\[ 1.68T - 476 = T \]

Subtract \(T\) from both sides:\[ 0.68T = 476 \]

Now, solve for \(T\):\[ T = \dfrac{476}{0.68} \]

\[ T \approx 700 \]

Therefore, the total number of votes polled is approximately 700. Hence, the correct answer is 700.

Let's denote the total number of votes polled as \(T\).

The candidate who secured 62% of the votes (let's call it \(V_1\)) received \(0.62T\) votes.

The margin of victory is given as 144 votes, so the votes received by the other candidate (\(V_2\)) is \(V_1 - 144\).

Now, we can set up an equation using the percentages and the total number of votes:\[ V_1 + V_2 = T \]

Substitute the expressions for \(V_1\) and \(V_2\):\[ 0.62T + (0.62T - 144) = T \]

Combine like terms:\[ 1.24T - 144 = T \]

Subtract \(T\) from both sides:\[ 0.24T = 144 \]

Now, solve for \(T\):\[ T = \dfrac{144}{0.24} \]

\[ T = 600 \]

Therefore, the total number of votes polled is 600. Hence, the correct answer is 600.

Let's denote the total number of valid votes as \( T \).

The candidate who got 38% of the votes (let's call it \( V_1 \)) received \( 0.38T \) votes.

The candidate who lost by 7200 votes got \( V_2 = V_1 - 7200 \) votes.

Now, we can set up an equation using the percentages and the total number of votes:\[ V_1 + V_2 = T \]

Substitute the expressions for \( V_1 \) and \( V_2 \):\[ 0.38T + (0.38T - 7200) = T \]

Combine like terms:\[ 0.76T - 7200 = T \]

Subtract \( T \) from both sides:\[ 0.24T = 7200 \]

Now, solve for \( T \):\[ T = \dfrac{7200}{0.24} \]

\[ T = 30000 \]

Therefore, the total number of valid votes was 30000. Hence, the correct answer is 30000.

Let's denote the total number of votes polled as \(T\).

The candidate who secured 40% of the votes (let's call it \(V_1\)) received \(0.40T\) votes.

The other candidate defeated the first candidate by a majority of 298 votes. Therefore, the votes received by the other candidate (\(V_2\)) is:\[ V_2 = V_1 + 298 \]

Now, we can set up an equation using the percentages and the total number of votes:\[ V_1 + V_2 = T \]

Substitute the expressions for \(V_1\) and \(V_2\):\[ 0.40T + (0.40T + 298) = T \]

Combine like terms:\[ 0.80T + 298 = T \]

Subtract \(0.80T\) from both sides:\[ 298 = 0.20T \]

Now, solve for \(T\):\[ T = \dfrac{298}{0.20} \]

\[ T = 1490 \]

Therefore, the total number of votes polled is 1490. Hence, the correct answer is 1490.

Let's denote the current number of females as \(F\) and the current number of males as \(M\). According to the information provided:

\[ F = 3000 \]

The total population is the sum of the number of females and males:

\[ \text{Total Population} = F + M \]

Given that the total population of the town is 9000:

\[ F + M = 9000 \]

Now, it's mentioned that the number of females increases by 5% and the number of males increases by 7.5%. The new number of females (\(F_{\text{new}}\)) and the new number of males (\(M_{\text{new}}\)) after the increase can be calculated as follows:

\[ F_{\text{new}} = F + 0.05F \]\[ M_{\text{new}} = M + 0.075M \]

Now, we can express the new total population (\(\text{Total Population}_{\text{new}}\)) after the increase:

\[ \text{Total Population}_{\text{new}} = F_{\text{new}} + M_{\text{new}} \]

Substitute the expressions for \(F_{\text{new}}\) and \(M_{\text{new}}\):

\[ \text{Total Population}_{\text{new}} = (F + 0.05F) + (M + 0.075M) \]

Combine like terms:

\[ \text{Total Population}_{\text{new}} = 1.05F + 1.075M \]

Given that \(F = 3000\) and \(F + M = 9000\), we can substitute these values into the equation:

\[ \text{Total Population}_{\text{new}} = 1.05 \times 3000 + 1.075 \times (9000 - 3000) \]

Calculate the expression:

\[ \text{Total Population}_{\text{new}} = 3150 + 1.075 \times 6000 \]

\[ \text{Total Population}_{\text{new}} = 3150 + 6450 \]

\[ \text{Total Population}_{\text{new}} = 9600 \]

Therefore, the total population after the increase is 9600. Hence, the correct answer is 9600.

Let's denote the present value of the scooter as \(P\). According to the given information, the value of the scooter decreases by 10% each year.

The value of the scooter after 1 year (\(P_1\)) can be calculated as:\[ P_1 = P - 0.10P = 0.90P \]

After the second year, the value (\(P_2\)) becomes:\[ P_2 = 0.90P - 0.10(0.90P) = 0.81P \]

After the third year, the value (\(P_3\)) becomes:\[ P_3 = 0.81P - 0.10(0.81P) = 0.729P \]

Now, we know the present value \(P\) is Rs. 7,290. Let's substitute this value into the equation:

\[ 0.729P = 7290 \]

Now, solve for \(P\):

\[ P = \dfrac{7290}{0.729} \]

\[ P = 10000 \]

Therefore, the value of the scooter 3 years back was Rs. 10,000. Hence, the correct answer is Rs. 10,000.