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A man sells three articles A, B and C and gains 10% on A, 20% on B and looses 10% on C. He breaks even when combined selling prices of A and C are considered. He gains 5% when combined prices of B and C are considered. What is his net loss or gain on the sale of all the articles.

So suppose the buying cost of A, B, C are a,b,c respectively. Now since he breaks even with selling A and C we have $$1.1a+0.9b=a+b$$ Also from second condition $$1.2b+0.9c=1.05(b+c)$$ Now we want to compute x such that $$1.1a+1.2b+0.9c=x(a+b+c)$$ How do I do this? I'm sure there is a simple step here but I cant seem to get it!

Capcom
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1 Answers1

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In your first equation, the $b$ should be a $c$.

Collecting terms with $a$ on the left side of the first equation and terms with $c$ on the right side, you will find that $a=c$. Similarly, from your second equation you will find that $b=c$. You can therefore write your last equation as: $$1.1a + 1.2a + 0.9a = x(a + a + a)$$

Divide by $a$ on both sides and you have your answer.

Jens
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