If the ratio of marked price and selling price of an article is 13:10. Shopkeeper earned 25% profit. If the difference between marked price and cost price of an article is Rs.450. find the selling price of an article.

The correct option is Rs.900.

Let us solve the problem step-by-step using ratios and basic percentage concepts.

Step 1: Understand the given ratios and relations.
We are given that the ratio of Marked Price (MP) to Selling Price (SP) is:
$\text{MP}:\text{SP}=13:10$

So, we can express MP and SP in terms of a constant $x$ as:
$\text{MP}=13x$
$\text{SP}=10x$

Step 2: Find the Cost Price (CP) in terms of $x$.
The shopkeeper earns a profit of 25%.
The relationship between Selling Price and Cost Price is given by:
$\text{SP}=\text{CP}\times \left(1+\frac{25}{100}\right)=\text{CP}\times \frac{125}{100}=\text{CP}\times \frac{5}{4}$

Now, substituting $\text{SP}=10x$ into the equation:
$10x=\text{CP}\times \frac{5}{4}$

Solving for CP:
$\text{CP}=10x\times \frac{4}{5}=8x$

Step 3: Use the difference between Marked Price and Cost Price to find $x$.
We are given that:
$\text{MP}-\text{CP}=450$

Substitute the values of MP and CP in terms of $x$:
$13x-8x=450$
$5x=450$
$x=90$

Step 4: Calculate the Selling Price (SP).
$\text{SP}=10x=10\times 90=900$

Thus, the selling price of the article is Rs.900.