Explanation

In a proportion of the form a : b :: c : d, the terms a and d are called the extremes, while b and c are called the means.

So, the ratio a : d (the first and the last terms) is called the Extreme Proportion.

Explanation

Cross multiply: 15 × 18 = 9 × x →270 = 9x

Divide both sides by 9: x = 30

Explanation

2 : 4 :: x : 40

This is a proportion, which means:

2 / 4 = x / 40

Now solve:

2 × 40 = 4 × x  

80 = 4x  

x = 80 / 4 = 20

Explanation

Calculating the Ratio of Capitals

Asad : Aamir = 63000 : 72000 = 7 : 8

Calculating the Profit Share

Total parts = 7 + 8 = 15

Aamir's share = 8/15 × 45000

= 8 × 3000

= 24000

Explanation

Calculating the Rate of Work per Man per Day

Rate = 630/70 × 5 = 630/350 = 1.8 m³/man/day

Calculating the Quantity of Soil for 80 Men in 10 Days

Quantity = 80 men × 10 days × 1.8 m³/man/day

= 80 × 10 × 1.8

= 1440 m³

Explanation

Calculating the Ratio

Passed students = 25

Total students = 45

Ratio = Passed students/Total students = 25/45 = 5/9 = 5:9

Explanation

To simplify the ratio 15:20, we need to find the greatest common divisor (GCD) of 15 and 20.

The GCD of 15 and 20 is 5.

Dividing both numbers by 5:

15 ÷ 5 = 3

20 ÷ 5 = 4

So, the simplest form of the ratio 15:20 is 3:4.

Explanation

Given A:B = 3:4 and B:C = 12:13.

First, make the ratios for B consistent:

A:B = 3:4 = 9:12 (multiplied by 3)

Now, B:C = 12:13

A:B:C = 9:12:13

A:C = 9:13

Explanation

Given the ratio of men to women is 3:5:

Step 1: Calculate the total parts in the ratio

Total parts = 3 + 5 = 8

Step 2: Determine the value of one part

Total people = 24

One part = 24 / 8 = 3

Step 3: Calculate the number of women

Number of women = 5 parts * 3

= 5 * 3

= 15

Explanation

 In the context of a ratio written as "a:b," the term 'a' is called the antecedent or the first term of the ratio, while 'b' is the consequent or second term. 

Antecedent: The first term or number in a ratio.

Consequent: The second term or number in a ratio. 

For example, in the ratio 5:2, the antecedent is 5, and the consequent is 2.