Explanation

Let's say B gets x amount. Then A gets 5/8 of x.

A's amount = (5/8)x

Total amount = A's amount + B's amount

338 = (5/8)x + x

Combine like terms:

338 = (5x + 8x)/8

338 = 13x/8

338 × 8 = 13x

2704 = 13x

x = 208

So B's amount is Rs. 208.

Explanation

Given:

a:b = 2:3

b:c = 5:3

First, make the b values equivalent:

a:b = 2:3 = 2 × 5 : 3 × 5 = 10:15

b:c = 5:3 = 5 × 3 : 3 × 3 = 15:9

Now, a:b:c = 10:15:9

Explanation

Step 1: Determine the total parts in the ratio

The ratio is 1:2:3, so the total parts are 1 + 2 + 3 = 6

Step 2: Calculate Noor's share

Noor's share is 1 out of 6 parts, so his share of the profit is (1/6) * 600

Step 3: Calculate the amount

(1/6) * 600 = 100

Explanation

Step 1: Convert both weights to the same unit

1 kg = 1000 g

3½ kg = 3.5 kg = 3.5 × 1000 g = 3500 g

Step 2: Calculate the ratio

Ratio = 3500 g : 50 g

= 3500 / 50

= 70

Step 3: Express the ratio in the required format

The ratio is 70:1.

Explanation

Total parts = 6 + 4 = 10; each part = 1300 ÷ 10 = Rs. 130

Smallest part = 4 × 130 = Rs. 520

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

Given CF = 24 and the centroid G divides CF in a 2:1 ratio, with the longer part toward the vertex C and the shorter part toward the midpoint F of side AB.

The total length CF is divided into 3 parts, where 2 parts are toward the vertex (CG) and 1 part is toward the midpoint (FG).

FG = (1/3) × CF = (1/3) × 24 = 8.

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

To find the fourth proportional, let's denote it as x. The proportion will be:

3 : 9 = 7 : x

We can cross-multiply:

3x = 9 × 7

3x = 63

x = 63 / 3

x = 21

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