Explanation

Let's denote the two numbers as 8x and 3x, where x is a common multiplier.

Given that their difference is 20:

8x - 3x = 20

5x = 20

x = 4

Now, let's find the numbers:

First number: 8x = 8 * 4 = 32

Second number: 3x = 3 * 4 = 12

Explanation

Explanation

Given:

105 increased in the ratio 9 : 7

To increase 105 in the ratio 9 : 7, we'll multiply 105 by 9/7:

New value = 105 × (9/7)

= 15 × 9

= 135

Explanation

Given:

g : h = 8 : 9

h : i = 9 : 12

To find the combined ratio g : h : i, we need to make the ratio of h the same in both.

g : h = 8 : 9

h : i = 9 : 12

Since h has the same ratio in both (9), we can directly combine:

g : h : i = 8 : 9 : 12

Explanation

Initially, the salaries are in the ratio 1:3:4. Let's assume the salaries are x, 3x, and 4x.

After the increases:

A's salary increases by 5%, so the new salary is x + 5% of x = x + 0.05x = 1.05x

B's salary increases by 10%, so the new salary is 3x + 10% of 3x = 3x + 0.10(3x) = 3.30x

C's salary increases by 15%, so the new salary is 4x + 15% of 4x = 4x + 0.15(4x) = 4.60x

Now, let's find the ratio of the increased salaries:

1.05x : 3.30x : 4.60x

To simplify, divide each term by 0.05x (the smallest common multiple):

1.05x / 0.05x = 21

3.30x / 0.05x = 66

4.60x / 0.05x = 92

So, the increased salaries are in the ratio 21:66:92.

Explanation

= 18 × 1/6

= 3

Explanation

To find the fourth proportional of 3, 7, and 15:

Let's denote the fourth proportional as x. We set up the proportion:

3/7 = 15/x

Step 1: Cross-multiply.

3x = 7 × 15

Step 2: Calculate the product of 7 and 15.

3x = 105

Step 3: Solve for x.

x = 105 / 3

x = 35

Explanation

Equating the two expressions and simplifying gives:

$$x cdot 200 = y cdot 250 Rightarrow frac{y}{x} = frac{200}{250} = frac{4}{5} Rightarrow y : x = 4 : 5$$

⇒y​/x=200/250

=4​/5

⇒y:x=4:5

Explanation

Explanation

Initial ratio: Boys:Girls = 8:5

After 22 more girls join:

Boys = 8x, Girls = 5x + 22 (where x is a constant)

Total students = 286 + 22 = 308

8x + 5x + 22 = 308

13x = 286

x = 22

Boys = 8x = 176

Girls = 5x + 22 = 132

New ratio = Boys:Girls = 176:132 = 4:3 (after simplification)