Question

If a : b = 4 : 5, b : c = 5 : 4 and c : d = 6 : 5, then a : b : c : d =

• A. 12 : 16 : 12 : 10
• B. 10 : 15 : 10 : 12
• C. 12 : 15 : 12 : 10
• D. 12 : 15 : 10 : 12

Hint:

When dealing with discrepancies in provisional answer keys, note down the exact steps.
To check options quickly, plug in the ratios:
If \(a:b = 4:5\), then the ratio of the first two terms must simplify to \(4:5\).
In Option (C) and (D), \(12:15\) simplifies to \(4:5\), matching our target.

Answer 1

The Correct Option is C

Step 1: Chain a:b and b:c.
a:b = 4:5 and b:c = 5:4. Since b = 5 in both, a:b:c = 4:5:4 directly.
Step 2: Incorporate c:d.
c:d = 6:5, but c = 4 in our chain. LCM(4, 6) = 12. Multiply a:b:c by 3 to make c = 12: gives 12:15:12. Multiply c:d by 2 to make c = 12: gives 12:10.
Step 3: Write the final ratio.
\[ a:b:c:d = 12:15:12:10 \] \[ \boxed{12:15:12:10} \]