Step-by-step Solution:

To solve this, we will represent the incomes and spendings using variables, find a relationship between these variables using the information about A's savings, and then calculate the savings for B and C to find the final ratio.

1. Set up expressions for income and spending:
Let the common ratio for incomes be \(x\) and for spendings be \(y\).
Incomes of A, B, C are \(7x, 9x, 12x\) respectively.
Spendings of A, B, C are \(8y, 9y, 15y\) respectively.

2. Use A's savings to find a relationship between x and y:
We know that Savings = Income - Spending.
Therefore, A's Savings = \(7x - 8y\).
We are also given that A saves \(1/4\) of his income:
A's Savings = \(\frac{1}{4} \times (7x) = \frac{7x}{4}\).
Now, we can set the two expressions for A's savings equal to each other to link \(x\) and \(y\):
\[\begin{aligned} 7x - 8y &= \frac{7x}{4} \\ 4(7x - 8y) &= 7x \\ 28x - 32y &= 7x \\ 21x &= 32y \\ y &= \frac{21x}{32} \end{aligned}\]
3. Calculate the savings for A, B, and C in terms of x:
Now we can express each person's savings using only the variable \(x\).
A's Savings = \(\frac{7x}{4}\)
B's Savings = \(9x - 9y = 9x - 9(\frac{21x}{32}) = 9x - \frac{189x}{32} = \frac{288x - 189x}{32} = \frac{99x}{32}\)
C's Savings = \(12x - 15y = 12x - 15(\frac{21x}{32}) = 12x - \frac{315x}{32} = \frac{384x - 315x}{32} = \frac{69x}{32}\)

4. Form and simplify the ratio of savings:
The ratio of savings for A:B:C is:
\[\frac{7x}{4} : \frac{99x}{32} : \frac{69x}{32}\]
First, cancel the common factor \(x\):
\[\frac{7}{4} : \frac{99}{32} : \frac{69}{32}\]
To remove the fractions, multiply all parts of the ratio by the least common denominator (which is 32):
\[(\frac{7}{4} \times 32) : (\frac{99}{32} \times 32) : (\frac{69}{32} \times 32)\]\[(7 \times 8) : 99 : 69\]\[56 : 99 : 69\]
Result:
The savings of A, B, and C are in the ratio 56:99:69.