A person marked up two articles, A & B, 20% & 25%, respectively, above their cost price & gave a discount of 15% on A & 10% on B. The difference between the selling prices of both the articles is Rs 618. Find the cost price (in Rs) of article B if the ratio of the cost prices of A & B is 4:5, respectively.

The correct option is 2000.

Step 1: Express the Cost Prices in terms of a variable
The ratio of the cost prices of articles A and B is given as 4 : 5.
Let the cost price of article A (${\mathrm{CP}}_A$) be $4x$ and the cost price of article B (${\mathrm{CP}}_B$) be $5x$.

Step 2: Calculate the Marked Price (MP) for both articles
Article A is marked up by 20% above its cost price:

${\mathrm{MP}}_A=4x\times (1+0.20)=4x\times 1.20=4.8x$

Article B is marked up by 25% above its cost price:

${\mathrm{MP}}_B=5x\times (1+0.25)=5x\times 1.25=6.25x$

Step 3: Calculate the Selling Price (SP) for both articles
A discount of 15% is given on article A:

${\mathrm{SP}}_A=4.8x\times (1-0.15)=4.8x\times 0.85=4.08x$

A discount of 10% is given on article B:

${\mathrm{SP}}_B=6.25x\times (1-0.10)=6.25x\times 0.90=5.625x$

Step 4: Equate the difference between the selling prices
The difference between the selling prices of the two articles is given as Rs 618:

${\mathrm{SP}}_B-{\mathrm{SP}}_A=618$

$5.625x-4.08x=618$

$1.545x=618$

$x=\frac{618}{1.545}=400$

Step 5: Determine the cost price of Article B
Substitute the value of $x$ back into the expression for ${\mathrm{CP}}_B$:

${\mathrm{CP}}_B=5x=5\times 400=2000$

Hence, the cost price of article B is Rs 2000.