How to find net loss or gain on the sale of all the particles

Question

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..

CY Aries · Accepted Answer · 2017-06-11T10:30:08.870

1

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

$$\frac{0.1a+0.2b-0.1c}{a+b+c}\times 100\%$$

edited Jun 11 '17 at 10:30

answered Jun 11 '17 at 10:20

CY Aries

23,393

I think the original prices have to be subtracted first before we can find the percentage gain. Also, the name percentage change will be more suitable unless we are sure that it is gain. – Mick Jun 11 '17 at 10:29
@Mick My mistake. Thanks for pointing out. – CY Aries Jun 11 '17 at 10:30
so the meaning of 'he breaks even when...' is the selling prices and total costs are equal?@CYAries – Mini_me Jun 11 '17 at 10:34
@mathiu_lady It should be. No gain, no loss – CY Aries Jun 11 '17 at 10:35
@CYAries Why in the second equation you have taken 1.05(b+c) in the r.h.s.? Here it is given 5% gain so it comes like .05(b+c) – Mini_me Jun 11 '17 at 10:38
The cost is $b+c$ and the gain is $0.05(b+c)$. So the selling price should be $1.05(b+c)$. – CY Aries Jun 11 '17 at 10:45
$a=b=c $ and the answer is $6.66%$ – alexjo Sep 10 '17 at 11:24

How to find net loss or gain on the sale of all the particles

1 Answers1