John sold an article to Peter at 20% profit and Peter sold it to Mohan at 5% loss. If Mohan paid ₹ 912 for the article, find how much did John pay for it?

Let the cost John paid for the article be ₹ $x$.

John sold the article to Peter at profit = 20%

As we know

$\text{Profit\%} = \dfrac{\text{Profit}}{\text{C.P.}} \times 100\\[1em] \Rightarrow 20 = \dfrac{\text{Profit}}{x} \times 100\\[1em] \Rightarrow \text{Profit} = \dfrac{20 \times x}{100}\\[1em] \Rightarrow \text{Profit} = \dfrac{x}{5}\\[1em]$

And

$\text{Profit = S.P. - C.P.}\\[1em] \Rightarrow \dfrac{x}{5} = S.P. - x\\[1em] \Rightarrow S.P. = \dfrac{x}{5} + x\\[1em] \Rightarrow S.P. = \dfrac{x}{5} + \dfrac{5x}{5}\\[1em] \Rightarrow S.P. = \dfrac{(x + 5x)}{5}\\[1em] \Rightarrow S.P. = \dfrac{6x}{5}\\[1em]$

Now, S.P. for John will be C.P. for Peter and Peter sold it to Mohan.

C.P. of the article for Peter = $\dfrac{6x}{5}$

Loss% of the article for Peter = 5%

S.P. of the article for Peter = ₹ 912

As we know

$\text{Loss\%} = \dfrac{\text{Loss}}{\text{C.P.}} \times 100\\[1em] \Rightarrow 5 = \dfrac{\text{Loss}}{\dfrac{6x}{5}} \times 100\\[1em] \Rightarrow \text{Loss} = \dfrac{5 \times 6x}{5 \times 100}\\[1em] \Rightarrow \text{Loss} = \dfrac{30x}{500}\\[1em] \Rightarrow \text{Loss} = \dfrac{3x}{50}\\[1em]$

And

$\text{Loss = C.P. - S.P.}\\[1em] \Rightarrow \dfrac{3x}{50} = \dfrac{6x}{5} - 912\\[1em] \Rightarrow \dfrac{6x}{5} - \dfrac{3x}{50} = 912\\[1em] \Rightarrow \dfrac{60x}{50} - \dfrac{3x}{50} = 912\\[1em] \Rightarrow \dfrac{(60x - 3x)}{50} = 912\\[1em] \Rightarrow \dfrac{57x}{50} = 912\\[1em] \Rightarrow x = \dfrac{912 \times 50}{57}\\[1em] \Rightarrow x = \dfrac{45,600}{57}\\[1em] \Rightarrow x = 800$

Hence, John paid ₹ 800 for the article.