X sold two cars at same price, one of them at 10% profit. x incurred total loss of 12% in overall transaction. what was the approximate profit/loss incurred on the other car?

You want to know the profit or loss incurred on the sale of a second car at the same price as a first car, if there was a 10% profit on the first car and a 12% overall loss on the sale of both cars.

Markup

For a given cost price (c) and markup multiplier (m), the selling price (s) is ...

s = c·m

This relation will hold for each sale, and for both sales together:

s = c₁·m₁
s = c₂·m₂
(2s) = (c₁ +c₂)·m₃

where ...

m₁ = 1.10 — a 10% profit on the first sale
m₃ = 0.88 — a 12% loss on both sales

Second markup

We can solve the first two equations for c₁ and c₂, then substitute into the third equation.

[tex]c_1=\dfrac{s}{m_1}=\dfrac{s}{1.10}\\\\\\c_2=\dfrac{s}{m_2}\\\\\\2s=\left(\dfrac{s}{1.10}+\dfrac{s}{m_2}\right)0.88\\\\\\\dfrac{2(1.10)(m_2)}{0.88}=m_2+1.10\\\\\\1.5m_2=1.1\\\\\\m_2=\dfrac{11}{15}=1-\dfrac{4}{15}\approx1-26.67\%[/tex]

The loss on the other car was about 26.67%.