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.

$\frac{100}{6}\%$

The correct answer is Option (2) → $\frac{100}{6}\%$

To find the profit percentage of the third seller, we can use the concept of successive percentage increases.

Step-by-Step Calculation:

1. Define the Initial Price: Let the initial cost price of the article be ₹100.

2. Calculate Price after the First Seller (15% Profit):

$\text{Price}_1​=100×(1+\frac{15}{100}​)=100×1.15=₹115$

3. Calculate Price after the Second Seller (20% Profit): The second seller earns 20% profit on the price they paid (₹115).

$\text{Price}_2​=115×(1+\frac{20}{100}​)=115×1.20=₹138$

4. Determine the Final Price (61% Overall Rise): The problem states that the price rises on the whole by 61% from the initial price.

$\text{Final Price}=100×(1+\frac{61}{100}​)=₹161$

5. Calculate the Third Seller's Profit: Let the third seller's profit percentage be x. The third seller bought the article for ₹138 and sold it for ₹161.

$\text{Profit}=161−138=₹23$

$\text{Profit Percentage (x)}=(\frac{\text{ Profit }}{\text{Cost Price for 3rd seller}} ​)×100$

$x=(\frac{23}{138}​)×100$

6. Simplify the Fraction: Divide both 23 and 138 by their greatest common divisor (which is 23):

$23÷23=1$

$138÷23=6$

$x=\frac{1}{6}​×100=\frac{100}{6}​\%$