Explanation

Let's denote the cost of one pizza as P and the cost of one donut as D.

From Farhan's purchase:

4P + 3D = 1670 ... (1)

From Hamid's purchase:

6P + 2D = 2280 ... (2)

We can multiply equation (1) by 2 and equation (2) by 3 to make the coefficients of D equal:

8P + 6D = 3340 ... (3)

18P + 6D = 6840 ... (4)

Now, subtract equation (3) from equation (4):

10P = 3500

P = 350

Explanation

Given:

Width = x

Length = 2 × Width = 2x

Perimeter of a rectangle = 2(Length + Width)

= 2(2x + x)

= 2(3x)

= 6x

Explanation

If 1 ¥ = 1.81 Pak rupees, then:

1 Pak rupee = 1 / 1.81 ¥

= 0.55 ¥

Explanation

To find the quotient, we need to divide the two fractions:

(64/63) ÷ (108/117)

= (64/63) × (117/108)

= (64 × 117) / (63 × 108)

= 7488 / 6804

= 208 / 189

Explanation

Valid Methods for Linear Equations:

Substitution: Solve one equation for a variable and substitute into the other.

Elimination: Add/subtract equations to eliminate a variable.

Cramer’s Rule: Uses determinants for systems with unique solutions.

Explanation

A cyclic quadrilateral is a four-sided figure where all vertices lie on the circumference of a single circle.

Key property: Opposite angles sum to 180°.

Explanation

A sector is a region of a circle enclosed by two radii and the arc between them.

Example: A pizza slice is a sector.

Explanation

To find the profit percentage:

Cost Price (CP) = Rs. 50

Selling Price (SP) = Rs. 75

Profit = SP - CP = 75 - 50 = Rs. 25

Profit Percentage = (Profit / CP) × 100

= (25 / 50) × 100

= 50%

Explanation

The expression {x|x ∈ A ∨ x ∈ B} represents the set of elements that are in A or in B or in both.

This is the definition of the union of two sets, denoted as A ∪ B.

Explanation

The square of 31 is:

31 × 31 = 961.