What is the smallest amount of the provision? Provisions for three companies totaling $ 48 million allocated in the ratio of 8:3:1. What is the smallest amount of the provision? This is my calculation: = 8 +3 +1 = 12 = 8x12: 3x12: 1x12 = 96: 36: 12 Provision of the smallest amount is **12 million**. => Refer to my exercise book, the answer is **4 million**. Are my calculations wrong?

We have the ratios of $8x : 3x: 1x$, where $x$ is in millions. That gives us a total of

$8x + 3x + 1\cdot x = 12x$ which is twelve _partitions_ of $48$ million: 12 groups of $x$-million.

So we can solve for $x$: $$12 x = 48 \;\text{million} \iff x = \dfrac{48\;\text{million}}{12} = 4 \;\text{million}$$

So that gives us a ratio of provisions with $$(8\cdot 4\;\text{million}) : (3\cdot 4\;\text{million}): (1 \cdot 4\;\text{million})$$

So the largest provision is $\;8\cdot 4 = 32 \;\text{million}$, and the smallest provision is $4$ million.