Explanation

The profit-sharing ratio between Hyder and Ahsan is 3:5.

The total parts are 3 + 5 = 8.

Ahsan's share is 5/8 of the total profit.

Given the total profit is 32,000:

Ahsan's share = (5/8) × 32,000

= 5 × 4000

= 20,000

Explanation

Let's call the marked price "x".

Since Saba got a 30% discount, she paid 70% of the marked price (100% - 30% = 70%).

The amount she paid is Rs. 6300, so:

70% of x = 6300

0.7x = 6300

x = 6300 / 0.7

x = 9000

Explanation

The given proportion is x : 72 :: 7 : 18.

This can be rewritten as x/72 = 7/18.

To find x, cross-multiply:

x × 18 = 7 × 72

18x = 504

x = 504 / 18

x = 28

Explanation

When two triangles have the same corresponding angles, they are said to be similar.

Similar triangles have the same shape but not necessarily the same size, meaning their corresponding angles are equal and their corresponding sides are proportional.

Explanation

Rise over run denotes the slope of a line. The slope formula is:

Slope = (y2 - y1) / (x2 - x1)

This is often referred to as "rise over run" because the numerator (y2 - y1) represents the vertical change (rise) and the denominator (x2 - x1) represents the horizontal change (run).

The answer is y2 - y1/x2 - x1.

Explanation

Supplementary angles add up to 180 degrees but aren't necessarily equal.

Supplementary angles can have various measures (e.g., 90° + 90°, 120° + 60°, 150° + 30°), showing they don't have to be equal.

Explanation

Let's find the square numbers between 63 and 143:

8² = 64 (since 8² = 64 > 63)

9² = 81

10² = 100

11² = 121

The next square number would be 12² = 144, which is greater than 143, so we stop at 11².

Now, let's calculate the sum:

64 + 81 + 100 + 121 = 366

Explanation

O(P) = O(Q) means the number of elements in P is equal to the number of elements in Q.

This implies that P and Q have the same cardinality, which can be represented as P ~ Q (P is equivalent to Q).

Explanation

Given:

a < b

b < c

Using transitive property, if a < b and b < c, then a < c.

Explanation

Let's multiply the fractions:

(9/4) × (-4/9) × 2/3

= (9 × -4 × 2) / (4 × 9 × 3)

= -72 / 108

= -2/3