If A : B = 8 : 13, B : C = 5 : 8 and C : D = 4 : 5, then A : B : C : D is equal to:

Given:

A : B = 8 : 13

B : C = 5 : 8

C : D = 4 : 5

Formula Used:

To find the combined ratio A : B : C : D, we need to express all given ratios with a common term and then combine them.

Calculation:

1. Start with A : B = 8 : 13

2. Express B : C = 5 : 8 with B being common in both ratios.

Since B is 13 in A : B = 8 : 13, we need to make B = 13 in B : C = 5 : 8.

⇒ Multiply B : C = 5 : 8 by 13/5 to make B = 13

⇒ B : C = 13 : (8 × 13 / 5)

⇒ B : C = 13 : 20.8

3. Express C : D = 4 : 5 with C being common in both ratios.

Since C is 20.8 in B : C = 13 : 20.8, we need to make C = 20.8 in C : D = 4 : 5.

⇒ Multiply C : D = 4 : 5 by 20.8/4 to make C = 20.8

⇒ C : D = 20.8 : (5 × 20.8 / 4)

⇒ C : D = 20.8 : 26

4. Now combine all ratios A : B : C : D

A : B = 8 : 13

B : C = 13 : 20.8

C : D = 20.8 : 26

⇒ A : B : C : D = 8 : 13 : 20.8 : 26

5. To make the ratio in whole numbers, multiply by 5

⇒ 8×5 : 13×5 : 20.8×5 : 26×5

⇒ 40 : 65 : 104 : 130

The correct answer is option 4.

Shortcut Trick