The average cost price of two articles, X and Y is Rs 1600. Article X is sold at a 15% profit, and article Y is sold at a 25% profit. The total selling price of articles X and Y is Rs 3800. If article Y is sold at a 50% profit, find the new selling price of article Y (in Rs).

The correct answer is 1800.

Let the cost price of article X be $x$ and the cost price of article Y be $y$.

We are given that the average cost price of the two articles is Rs 1600. Therefore, the sum of their cost prices can be written as:

$\frac{x+y}{2}=1600$

Multiplying both sides by 2, we get:

$x+y=3200$     — (Equation 1)

Next, we are given the selling prices of the two articles under the first scenario:
- Article X is sold at a 15% profit, which means its selling price is $1.15x$.
- Article Y is sold at a 25% profit, which means its selling price is $1.25y$.

The total selling price of both articles is Rs 3800. This gives us the equation:

$1.15x+1.25y=3800$    — (Equation 2)

To solve for $y$, we can multiply Equation 1 by 1.15 to match the coefficient of $x$:

$1.15(x+y)=1.15\times 3200$

$1.15x+1.15y=3680$    — (Equation 3)

Now, subtract Equation 3 from Equation 2 to eliminate $x$:

$(1.15x+1.25y)-(1.15x+1.15y)=3800-3680$

$0.10y=120$

$y=\frac{120}{0.10}=1200$

So, the cost price of article Y is Rs 1200.

If article Y is sold at a 50% profit, the new selling price of article Y is calculated as:

$\text{New Selling Price of Y}=\text{Cost Price of Y}\times (1+0.50)$

$\text{New Selling Price of Y}=1200\times 1.50=1800$

Thus, the new selling price of article Y is Rs 1800.