Explanation

Explanation

Let's denote the two parts as x and 12 - x.

The sum of their squares is x² + (12 - x)².

Twice their product is 2x(12 - x).

According to the problem:

x² + (12 - x)² - 2x(12 - x) = 4

x² + 144 - 24x + x² - 24x + 2x² = 4

4x² - 48x + 140 = 0

x² - 12x + 35 = 0

(x - 7)(x - 5) = 0

x = 7 or x = 5

The two parts are 5 and 7.

Let's check:

5² + 7² = 25 + 49 = 74

2 × 5 × 7 = 70

74 - 70 = 4

This satisfies the condition.

The answer is 5 and 7.

Explanation

Total workers = 120

Women = 45

Men = 120 − 45 = 75

Now, the ratio of men to women = 75 : 45

Simplify by dividing both by 15:

75 ÷ 15 = 5

45 ÷ 15 = 3

The ratio of men to women is 5:3.

Explanation

Let the money Bilal has = x

Then Ahmed has = x + 20

Together they have:

x + (x + 20) = 150

→ 2x + 20 = 150

→ 2x = 130

→ x = 65

Bilal has 65 PKR.

Explanation

To find when Mubashir and Ali will both exercise on the same day again, we need to calculate the Least Common Multiple (LCM) of their exercise days:

Mubashir: every 8 days

Ali: every 4 days

LCM of 8 and 4 = 8

They will both exercise again on the same day after 8 days.

Explanation

Let's find the expense per guest:

Expense for 35 guests = 52,500

Expense per guest = 52,500 / 35

= 1,500

Expense for 85 guests:

= 85 × 1,500

= 127,500

Explanation

Let's denote the width as w and the length as 3w (since the length is thrice the width).

The area of the window is:

w × 3w = 3w²

Given area = 18.75 sqm

3w² = 18.75

w² = 18.75 / 3

w² = 6.25

w = √6.25

w = 2.5

Length = 3w

= 3 × 2.5

= 7.5

Explanation

To find the greatest length of a tape that can measure both 52 m and 36 m exactly, we need the HCF (Highest Common Factor) of 52 and 36.

Step-by-step:

Factors of 52: 1, 2, 4, 13, 26, 52

Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36

Common factors: 1, 2, 4

Greatest common factor = 4

Explanation

Let's find the cloth required per dress:

20 meters / 4 dresses = 5 meters/dress

For 15 dresses:

15 dresses × 5 meters/dress = 75 meters

Explanation