Step-by-step explanation:

Let's denote the cost price of the article as(C)

Selling price with a 10% profit: (C + 0.10C = 1.10C).

If he had bought it at 20% less (0.80C) and sold it for 10 more (1.10C + 10), he would have earned a profit of 40%.

Setting up the equation: (1.10C + 10 = 1.40(0.80C)).

Sure, let's solve the equation:

[tex]\[1.10C + 10 = 1.40(0.80C)\][/tex]

Distribute on the right side:

[tex]\[1.10C + 10 = 1.12C\][/tex]

[tex]Subtract \: (1.10C) \: from \: both \: sides:[/tex]

[tex]\[10 = 0.02C\][/tex]

Now, divide both sides by (0.02) to find the value of (C):

[tex]\[C = \frac{10}{0.02} = 500\][/tex]

So, the original cost price (C) of the article is 500.

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[tex]\Large{\mathbb{\colorbox{beige}{\color{gold}{ANSWER}}}}[/tex]

Let's denote the cost price of the article as(C)

Selling price with a 10% profit: (C + 0.10C = 1.10C).

If he had bought it at 20% less (0.80C) and sold it for 10 more (1.10C + 10), he would have earned a profit of 40%.

Setting up the equation: (1.10C + 10 = 1.40(0.80C)).

Sure, let's solve the equation:

[tex]1.10C+10=1.40(0.80C)[/tex]

Distribute on the right side:

[tex]1.10C+10=1.12C[/tex]

[tex]Subtract \: (1.10C) \: from \: bothsides[/tex]

[tex]10=0.02C[/tex]

Now, divide both sides by (0.02) to find the value of (C):

[tex]c = \frac{10}{0.02} = 500[/tex]

So, the original cost price (C) of the article is 500.

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[tex]\scriptsize{\tt{Hope \: it \: helps \: you!!!}}[/tex]