Sold two articles gaining $20$% on one and losing $20$% on the other. What is the total gain/loss?

Question

Here is a problem,,

Kethy sold two articles on one she gains $20$% and on the other $20$% loss. Find how much she gains or she lose if cost price of one is $50$% the other.

Multiple choices are correct...

Options:

1. $\frac{20}{3}$ profit
2. $\frac{20}{3}$ loss
3. $\frac{140}{23}$ profit
4. $4$% profit
5. $4$% loss

Progress

I have considered one as 50 and other 100, and able to compute profit,..stuck at 20/3 loss but never able to prove 3rd one as correct option...(this book is full of mistakes)

Answer 1

Let's assume, as you did, that she paid 50 for the first item and 100 for the second item.

Then she either sold the first item for 40 and the second item for 120, or

she sold the first item for 60 and the second item for 80.

In the first case, she has a gain of 10, and in the second case she has a loss of 10;

so she has either a gain or a loss of $\frac{10}{150}=\frac{1}{15}=\frac{100}{15}\%=\frac{20}{3}\%$.