The price of an article, passing through three hands, rises on the whole by 61%, if the first and the second sellers earned 15% and 20% profit respectively, find the percentage profit earned by the third seller.

An article is sold through 3 sellers. Each seller buys it and then sells it at a profit:

• 1st seller makes 15% profit
• 2nd seller makes 20% profit
• 3rd seller makes unknown profit
• Overall increase is 61% from original price to final price

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Let the original cost price be $100$.

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The 1st seller earns 15% profit.

Price after 1st seller $= 100 \times (1 + \dfrac{15}{100})$

$= 100 \times 1.15$

$= 115$

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The 2nd seller earns 20% profit on $115$.

Price after 2nd seller $= 115 \times (1 + \dfrac{20}{100})$

$= 115 \times 1.20$

$= 138$

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The overall increase is 61% from the original price.

Final Price $= 100 \times (1 + \dfrac{61}{100})$

$= 100 \times 1.61$

$= 161$

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The 3rd seller buys at $138$ and sells at $161$.

Let the profit percentage be $x\%$.

$138 \times (1 + \dfrac{x}{100}) = 161$

$1 + \dfrac{x}{100} = \dfrac{161}{138}$

$\dfrac{x}{100} = \dfrac{161}{138} - 1$

$\dfrac{x}{100} = \dfrac{161 - 138}{138}$

$\dfrac{x}{100} = \dfrac{23}{138}$

$x = \dfrac{2300}{138}$

$x = \dfrac{50}{3}$

$x = 16\dfrac{2}{3}\%$

Therefore, the third seller earned a profit of $\dfrac{100}{6}\%$.