A man sells three articles A, B, C and gains 10% on A, 20% on B and loses 10% on C. He breaks even when combined selling prices of A and C are considered, whereas he gains 5% when combined selling prices of B and C are considered. What is his net loss or gain on the sale of all the articles?
I cannot understand the bold written part. Calculating for the gain of 5% when combined selling prices of B and C are considered, I get that the prices(actual) of B and C are same. But with this I can't find the net loss or gain on the sale of all the particles.
Need some help please..
If $a$, $b$ and $c$ are the costs of $A$, $B$ and $C$ respectively. Then the selling prices are $1.1a$, $1.2b$ and $0.9c$ respectively. So we have
$$1.1a+0.9c=a+c$$
and
$$1.2b+0.9c=1.05(b+c)$$
So we can express $b$ and $c$ in terms of $a$.
The percentage gain on the sale of all the articles is
$$\frac{0.1a+0.2b-0.1c}{a+b+c}\times 100\%$$