Explanation

To convert km/h to m/s:

1 km = 1000 m

1 hour = 3600 seconds

So, 180 km/h = 180 × (1000 m / 1 km) × (1 hour / 3600 seconds)

= 180 × 1000 / 3600

= 50 m/s

Explanation

A pie chart represents 360°, so the proportion is (60° / 360°) × 100 = 16.66%.

This means the given sector covers 1/6th of the total pie chart.

Explanation

Direct Proportion:

When a decrease in one quantity causes a proportional decrease in another, they are directly related.

Example: If you reduce the number of workers, the amount of work done decreases proportionally.

Rate: Measures change over time (e.g., speed).

Ratio: Compares quantities without implying proportionality.

Inverse Proportion: Increase in one causes decrease in the other (e.g., speed vs. time).

Explanation

Given Data:

m∠B = 120°

Ratio of m∠A : m∠C = 5 : 7

Step-by-Step Solution:

Triangle Angle Sum Property:

m∠A + m∠B + m∠C = 180°

m∠A + 120° + m∠C = 180°

m∠A + m∠C = 60°

Solving Using Ratio:

Let m∠A = 5x and m∠C = 7x

5x + 7x = 60

12x = 60

x = 5

Finding m∠A:

m∠A = 5 × 5 = 25°

Explanation

To find the profit percentage:

Profit = Sale Price - Cost Price

= 2700 - 2500

= 200

Profit Percentage = (Profit / Cost Price) × 100

= (200 / 2500) × 100

= 8%

Explanation

Step-by-step binary addition:

1 + 1 = 10 (0, carry 1)

0 + 1 + 1 (carry) = 10 (0, carry 1)

1 + 1 + 1 (carry) = 11 (1, carry 1)

Final result: (1100)₂

Explanation

Factor the numerator:

(a² - b²) = (a + b)(a - b)

Now, divide by (a + b):

[(a + b)(a - b)] ÷ (a + b)

= (a - b)

Explanation

Like terms are terms that have the same variable(s) with the same exponent(s).

x² and - √3x² are like terms because they both have the same variable (x) with the same exponent (²).

Explanation

To find the greatest number of students that can accommodate 135, 180, and 225 completely, we need to find the Highest Common Factor (HCF) of these numbers.

Step 1: Prime Factorization

135 = 3³ × 5

180 = 2² × 3² × 5

225 = 3² × 5²

Step 2: Identify Common Factors

Common factors = 3² × 5 = 9 × 5 = 45

Explanation

We use the unitary method:

Cost of 30 kg sugar = Rs. 1200

Cost of 1 kg sugar = 1200 ÷ 30 = Rs. 40

Cost of 35 kg sugar = 40 × 35 = Rs. 1400