Question

If A : B = 2 : 3, B : C = 4:5 and C : D = 6 : 7, then find the value of A : B : C : D

• A. 8 : 12 : 30 : 35
• B. 16 : 24 : 30 : 35
• C. 12 : 18 : 30 : 35
• D. 4 : 24 : 30 : 35

Answer 1

Answer:

B. 16 : 24 : 30 : 35

1. Combine A:B and B:C to find A:B:C:

   • Given A : B = 2 : 3 and B : C = 4 : 5.

   • Identify the common term, which is B. The values for B are 3 and 4.

   • Find the Least Common Multiple (LCM) of 3 and 4, which is 12.

   • Adjust the first ratio: To make B equal to 12, multiply A:B by 4. So, A : B = (2 × 4) : (3 × 4) = 8 : 12.

   • Adjust the second ratio: To make B equal to 12, multiply B:C by 3. So, B : C = (4 × 3) : (5 × 3) = 12 : 15.

   • Now, since the B terms are equal, we can combine them: A : B : C = 8 : 12 : 15.

2. Combine A:B:C and C:D to find A:B:C:D:

   • We have A : B : C = 8 : 12 : 15 and C : D = 6 : 7.

   • Identify the common term, which is C. The values for C are 15 and 6.

   • Find the LCM of 15 and 6, which is 30.

   • Adjust the combined ratio: To make C equal to 30, multiply A:B:C by 2. So, A : B : C = (8 × 2) : (12 × 2) : (15 × 2) = 16 : 24 : 30.

   • Adjust the last ratio: To make C equal to 30, multiply C:D by 5. So, C : D = (6 × 5) : (7 × 5) = 30 : 35.

   • Finally, combine them: A : B : C : D = 16 : 24 : 30 : 35.