Explanation

A/B = 2/3

B/C = 3/4

A/D = 4/5

We can start by finding the relationship between B and D:

B/A = 3/2 (inverse of A/B)

A/D = 4/5

Multiplying these two fractions, we get:

B/D = (3/2) × (4/5) = 12/10 = 6/5

Now, we can find C/D:

C/D = (C/B) × (B/D)

= (4/3) × (6/5)

= 8/5

Explanation

Step 1: Understand the meaning

We are given two ratios and asked to find a common multiple — that is, a set of values for M, N, and O that fits both ratios proportionally.

Given Ratios:

1. M : N : O = 2 : 3 : 5

2. M : N : O = 4 : 5 : 6

We want to find a new ratio X : Y : Z that is proportional to both these given ratios.

Step 2: Check Option B: 8:15:30

Try simplifying 8:15:30:

Divide all terms by 1 (GCD is 1, so already simplified):
Still 8:15:30

Now check if it fits the first ratio (2:3:5):

• 8 ÷ 2 = 4

• 15 ÷ 3 = 5

• 30 ÷ 5 = 6

So 8:15:30 = 2×4: 3×5: 5×6 = 2:3:5 scaled up by different amounts?
No — wait! Those aren’t consistent scalings.

Instead, let’s try another way:

Divide 8:15:30 by 4:

• 8 ÷ 4 = 2

• 15 ÷ 5 = 3

• 30 ÷ 6 = 5

So 8:15:30 → 2:3:5  (matches first ratio)

Now divide 8:15:30 by 2:

• 8 ÷ 2 = 4

• 15 ÷ 3 = 5

• 30 ÷ 5 = 6

So 8:15:30 → 4:5:6  (matches second ratio)

8:15:30 is a common multiple of both 2:3:5 and 4:5:6

Explanation

A : B = 2 : 3

B : C = 4 : 5

Calculation :

A : B = 2 : 3 ---- (1) × 4

B : C = 4 : 5 ---- (2) × 3

Multiply by 4 in equation (1) and multiply by 3 in equation (2)

∴ A : B : C = 8 : 12 : 15

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

Explanation

Given that 40% of a number is equal to two-third of another number, we need to find the ratio of the first number to the second number.

Let's assume that the first number is x and the second number is y. 40% of x is equal to 2/3 of y.

We can write this as: 0.4x = 2/3 y To find the ratio of x to y, we can divide both sides by y: 0.4x/y = 2/3

Simplifying further, we get: x/y = (2/3)/(0.4) x/y = 5/3

Therefore, the ratio of the first number to the second number is 5:3.

Explanation

To find the new quantity of cupcakes, let's calculate based on the given ratio of 7:6.

Initial quantity = 360 cupcakes

Ratio increase = 7:6

New quantity = 360 × (7/6) = 420 cupcakes

Explanation

Given proportion:

4 : 3 = 8 : p

First, let's find the relationship between 4 and 8:

8 = 2 * 4

Now, apply the same relationship to 3:

p = 2 * 3

p = 6

Explanation

Given the calculation:

70 decreased in 2:5

New value = 70 * (2/5)

= 70 * 0.4

= 28

Explanation

Given:

Hyder’s investment = Rs. 90,000

Ahsan’s investment = Rs. 60,000

Total profit = Rs. 45,000

Step 1: Find the ratio of their investments

Hyder : Ahsan = 90,000 : 60,000 = 3 : 2

Step 2: Divide the profit in the ratio 3:2

Total parts = 3 + 2 = 5

Ahsan’s share = (2/5) × 45,000 = Rs. 18,000