Question

If \( A : B = 3 : 4 \) and \( B : C = 5 : 7 \), then \( A : B : C \) is equal to

• A. 8 : 12 : 18
• B. 6 : 9 : 13
• C. 6 : 9 : 26
• D. 15 : 20 : 28

Answer 1

The Correct Option is D

To combine the ratios, first express \( B \) in the same terms for both ratios: \[ A : B = 3 : 4 \quad and \quad B : C = 5 : 7 \] Multiply the first ratio by 5 and the second by 4 to make \( B \) the same: \[ A : B = 15 : 20 \quad and \quad B : C = 20 : 28 \] Therefore, \( A : B : C = 15 : 20 : 28 \). 
To combine two ratios, make sure the common term (in this case, \( B \)) is the same by multiplying both ratios appropriately.