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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?

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up vote 3 down vote accepted

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.

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Needs a TU +1 ... – Amzoti Jul 21 '13 at 0:24
Needs another + too :-) – Babak S. Jul 21 '13 at 8:34

It's incorrect to multiply by $8+3+1=12$

Actually, the smallest amount of the provision $$=\frac 1{(8+3+1)}\cdot 48\text{ million }=??$$

Alternately, let the highest common factor of each company $=x$ million

So, $8x+3x+x=48\implies x=4$

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