Percentage All Competence Aptitude

Let's denote A's income as \( A \) and B's income as \( B \). Given that A's income is 50% less than B's income, it means \( A = B - 0.50B \). Now, simplify the expression for A: \[ A = 0.50B \] To find the percentage by which B's income is more than A's, we can use the formula: \[ \text{Percentage Increase} = \left( \dfrac{\text{Increase}}{\text{Original Value}} \right) \times 100 \] The increase is \( B - A \), and the original value is \( A \). \[ \text{Percentage Increase} = \left( \dfrac{B - A}{A} \right) \times 100 \] Substitute the expression for \( A \) from above: \[ \text{Percentage Increase} = \left( \dfrac{B - 0.50B}{0.50B} \right) \times 100 \] Simplify the expression: \[ \text{Percentage Increase} = \left( \dfrac{0.50B}{0.50B} \right) \times 100 \] Cancel out the common factor: \[ \text{Percentage Increase} = 100 \] Therefore, B's income is 100% more than A's income. Hence, the correct answer is 100%.

Let's denote the basic pay as \( x \).

According to the given information, the allowances of an employee constitute 165% of his basic pay:

\[ \text{Allowances} = 1.65x \]

Now, the gross salary is the sum of the basic pay and allowances:

\[ \text{Gross Salary} = x + \text{Allowances} \]

Given that the gross salary is 11925:

\[ 11925 = x + 1.65x \]

Combine like terms:

\[ 11925 = 2.65x \]

Now, solve for \( x \):

\[ x = \dfrac{11925}{2.65} \]

\[ x \approx 4500 \]

Therefore, the basic pay is 4500.

So, the correct answer is 4500.

Let's assume Nitin's original salary is \( x \).

1. Nitin's salary reduced by 10%: \( x - 0.10x = 0.90x \)
2. The reduced salary increased by 10%: \( 0.90x + 0.10(0.90x) = 0.99x \)

Now, let's compare the new salary with the original salary:

\[ \text{Percentage change} = \left( \dfrac{\text{Change in salary}}{\text{Original salary}} \right) \times 100 \]

\[ \text{Percentage change} = \left( \dfrac{0.99x - x}{x} \right) \times 100 \]

\[ \text{Percentage change} = -1\% \]

Therefore, the new salary is 1% less than the original salary.

So, the correct answer is 1% less.

Let's assume A's monthly salary is \( S \).

A saves 20% of his monthly salary, which is \( 0.20S \).

Given that his monthly expenditure is \( 6,000 \), his monthly savings (\( S_{\text{savings}} \)) can be expressed as:

\[ S_{\text{savings}} = 0.20S = S - 6,000 \]

Now, solve for \( S \):

\[ 0.20S = S - 6,000 \]

Subtract \( 0.20S \) from both sides:

\[ 0.80S = 6,000 \]

Divide by \( 0.80 \) to solve for \( S \):

\[ S = \dfrac{6,000}{0.80} \]

\[ S = 7,500 \]

Now, calculate the monthly savings (\( 0.20S \)):

\[ \text{Monthly savings} = 0.20 \times 7,500 = 1,500 \]

Therefore, A's monthly savings are \( 1,500 \).

So, the correct answer is \( 1,500 \).

Let's assume the man's income is \( I \).

According to the given information, the man spends 15% of his income, which is \( 0.15I \).

Given that his expenditure is Rs. 75, we can set up the equation:

\[ 0.15I = 75 \]

Now, solve for \( I \):

\[ I = \dfrac{75}{0.15} \]

\[ I = 500 \]

Therefore, the man's income is Rs. 500.

So, the correct answer is 500.

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

According to the given information, A's salary is 30% more than that of B:

\[ A = x + 0.30x = 1.30x \]

Now, we want to find by how much percent B's salary is less than that of A:

\[ \text{Percentage less than } A = \left( \dfrac{x}{1.30x} \right) \times 100 \]

Simplify the expression:

\[ \text{Percentage less than } A = \left( \dfrac{1}{1.30} \right) \times 100 \]

\[ \text{Percentage less than } A \approx 76.92\% \]

Therefore, B's salary is approximately 76.92% less than that of A.

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

\[ 100\% - 76.92\% \approx 23.08\% \]

So, by approximately 23.08%, B's salary is less than that of A.

Therefore, the correct answer is 23.08%.

Let's denote the two numbers as \( 2x \) and \( 3x \), where \( x \) is a positive constant.

According to the given information:

1. \( 20\% \) of the smaller number added to \( 20 \) is equal to the sum of \( 10\% \) of the larger number and \( 25 \):

   \[ 0.2(2x) + 20 = 0.1(3x) + 25 \]

   Simplify and solve for \( x \):

   \[ 0.4x + 20 = 0.3x + 25 \]

   \[ 0.1x = 5 \]

   \[ x = 50 \]

Now that we know \( x = 50 \), we can find the smaller number:

\[ \text{Smaller number} = 2x = 2 \times 50 = 100 \]

Therefore, the smaller number is 100. Hence, the correct answer is \( \boxed{100} \).

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

According to the given information:

1. The ratio of the number of boys to girls is \(3:2\).
2. 20% of the boys are scholarship holders, and 30% of the girls are scholarship holders.

First, let's find the number of scholarship holders:

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

Number of girls with scholarship = \(0.30 \times 2x = 0.6x\)

Now, the total number of students with scholarships is \(0.6x + 0.6x = 1.2x\).

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

The percentage of students with scholarships is \(\dfrac{1.2x}{5x} \times 100\% = 24\%\).

Therefore, the percentage of students who do not get a scholarship is \(100\% - 24\% = 76\%\).

Hence, the correct answer is \( \boxed{76\%} \).

Let's denote the two numbers as \(a\) and \(b\), where \(a\) is the larger number and \(b\) is the smaller number. The given information can be expressed as:

\[ a - b = 0.15(a + b) \]

Now, let's solve this equation to find the relationship between \(a\) and \(b\):

\[ a - b = 0.15a + 0.15b \]

Combine like terms:

\[ 0.85a = 1.15b \]

Now, find the ratio of the larger number to the smaller number:

\[ \dfrac{a}{b} = \dfrac{1.15b}{0.85a} \]

Multiply both sides by \( \dfrac{100}{15} \) to simplify the ratio:

\[ \dfrac{a}{b} = \dfrac{23}{17} \]

Therefore, the correct ratio of the larger number to the smaller number is \( \boxed{23 : 17} \).

Let's denote A's income as \( A \) and B's income as \( B \). The given information can be expressed as:

\[ 0.35A = 0.25B \]

Now, let's solve for the ratio of A's income to B's income:

\[ \dfrac{A}{B} = \dfrac{0.25B}{0.35A} \]

Multiply both sides by \( \dfrac{100}{25} \) to simplify the ratio:

\[ \dfrac{A}{B} = \dfrac{1}{1.4} \]

Multiply the numerator and denominator by 5 to get rid of the decimal:

\[ \dfrac{A}{B} = \dfrac{5}{7} \]

Therefore, the correct ratio of A's income to B's income is \( \boxed{5 : 7} \).