If (a-b) : (b-c) : (c-d) = 1 : 2 : 3 then what is the value of (a + d) : c ?
2:1
We are given (a − b) : (b − c) : (c − d) = 1 : 2 : 3. Introduce a common unit k:
a − b = k, b − c = 2k, c − d = 3k.
These involve four unknowns but only differences, so we may fix one value freely. Take the smallest, d = 0.
Then c − d = 3k gives c = 3k.
b − c = 2k gives b = c + 2k = 3k + 2k = 5k.
a − b = k gives a = b + k = 5k + k = 6k.
Now form the required ratio:
(a + d) : c = (6k + 0) : 3k = 6k : 3k = 2 : 1.
The answer is independent of the value chosen for d because it is a ratio. The results 1:2, 4:1 and 3:1 come from mis-adding the differences or forgetting that only gaps, not absolute values, are fixed.
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