Explanation

Let's find the fourth proportional.

If 8 : 4 :: 2 : x, then

8/4 = 2/x

2 = 2/x

x = 1

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

Given:

2 : 5 = 6 : x

We can write it as:

2/5 = 6/x

Cross-multiplying:

2x = 6 × 5

2x = 30

x = 30/2

x = 15

Explanation

Explanation

Given the proportion:

6 : x :: 9 : 12

We can write it as:

6/x = 9/12

Cross-multiplying:

6 × 12 = 9 × x

72 = 9x

x = 72/9

x = 8

Explanation

Given proportion:

2 : 7 :: 14 : x

We can set up an equation based on the proportion:

2/7 = 14/x

Cross-multiplying:

2x = 14 × 7

2x = 98

Dividing both sides by 2:

x = 98/2

x = 49

Explanation

In direct proportion, both quantities increase or decrease together at the same rate.

In inverse proportion, when one quantity increases, the other decreases in the same ratio.

Explanation

Given:

(x + 5) : (x + 7) = 5 : 7

We can write it as:

(x + 5) / (x + 7) = 5/7

Cross-multiplying:

7(x + 5) = 5(x + 7)

7x + 35 = 5x + 35

7x - 5x = 35 - 35

2x = 0

x = 0

Explanation

Total parts = 2 + 3 + 5 = 10

Salma's share = (2/10) × 2000 = 400.

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