A shopkeeper marks up an article by 60% on its cost price. He allows a discount of 25% on the marked price. If the selling price of the article is Rs 900, then find the cost price (in Rs).

The correct answer is 750.

To find the cost price of the article, let us break down the problem step-by-step.

First, let the Cost Price of the article be represented as $\mathrm{CP}$.

The shopkeeper marks up the article by 60% on its cost price.
Therefore, the Marked Price (MP) can be calculated as:
$\mathrm{MP}=\mathrm{CP}+0.60\times \mathrm{CP}$
$\mathrm{MP}=1.6\times \mathrm{CP}$

Next, the shopkeeper allows a discount of 25% on this marked price.
Therefore, the Selling Price (SP) is:
$\mathrm{SP}=\mathrm{MP}-0.25\times \mathrm{MP}$
$\mathrm{SP}=0.75\times \mathrm{MP}$

Substituting the expression for MP in terms of CP into the selling price equation:
$\mathrm{SP}=0.75\times (1.6\times \mathrm{CP})$
$\mathrm{SP}=1.2\times \mathrm{CP}$

We are given that the selling price of the article is Rs 900.
Setting up the equation:
$1.2\times \mathrm{CP}=900$

Solving for CP:
$\mathrm{CP}=\frac{900}{1.2}$
$\mathrm{CP}=750$

Thus, the cost price of the article is Rs 750.