A person buys three articles P, Q and R for ` 3,330. If P costs 25% more than R and R costs 20% more than Q, then what is the cost of P?

The correct option is ₹ 1,350.

Let us break down the solution step-by-step to understand how we arrive at the cost of P.

Step 1: Understand the relationships between the costs of the articles
Let the cost price of article Q be represented as $q$.
We are given that R costs 20% more than Q. Therefore, the cost price of R (let's call it $r$) can be written in terms of $q$ as:
$r=q+0.20q=1.20q$

Next, we are given that P costs 25% more than R. Therefore, the cost price of P (let's call it $p$) in terms of $r$ is:
$p=r+0.25r=1.25r$

Step 2: Express the cost of P in terms of Q
Now, substitute the value of $r$ from the first equation into the equation for $p$:
$p=1.25\times \left(1.20q\right)$
Calculating the product:
$p=1.5q$

Step 3: Use the total cost of all three articles
The total cost of P, Q, and R is given as ₹ 3,330.
So, we can write:
$p+q+r=3330$

Now, express all costs in terms of $q$:
$1.5q+q+1.2q=3330$

Combine the like terms on the left side:
$(1.5+1+1.2)q=3330$
$3.7q=3330$

Step 4: Solve for the cost of Q
$q=\frac{3330}{3.7}$
Multiplying numerator and denominator by 10 to clear the decimal:
$q=\frac{33300}{37}$
Dividing 33300 by 37:
$q=900$

So, the cost price of article Q is ₹ 900.

Step 5: Calculate the cost of P
Using the relation we established in Step 2:
$p=1.5q$
$p=1.5\times 900$
$p=1350$

Thus, the cost of P is ₹ 1,350.