A wholesaler marks up goods by 50% and gives 12% trade discount. Retailer marks up by 20% and offers 8% discount. Customer pays ₹12,216. What is wholesaler's cost price approximately?

Correct Answer: The correct option is ₹8,383.

Step-by-Step Explanation:

Step 1: Understand the chain of transactions
1. Wholesaler has a Cost Price (${\mathrm{CP}}_W$).
2. Wholesaler marks up the price by 50% to get their Marked Price (${\mathrm{MP}}_W$).
3. Wholesaler gives a 12% trade discount on ${\mathrm{MP}}_W$ to sell it to the Retailer. This Selling Price of the Wholesaler (${\mathrm{SP}}_W$) is the Cost Price for the Retailer (${\mathrm{CP}}_R$).
4. Retailer marks up their cost price by 20% to get their Marked Price (${\mathrm{MP}}_R$).
5. Retailer offers an 8% discount on ${\mathrm{MP}}_R$ to the Customer.
6. Customer pays ₹12,216 for the goods.

Step 2: Express each stage mathematically

Let the cost price of the wholesaler be $x$.

1. Wholesaler's Marked Price (${\mathrm{MP}}_W$):

${\mathrm{MP}}_W=x\times (1+0.50)=1.50x$

2. Wholesaler's Selling Price / Retailer's Cost Price (${\mathrm{CP}}_R$):

${\mathrm{CP}}_R={\mathrm{MP}}_W\times (1-0.12)=1.50x\times 0.88=1.32x$

3. Retailer's Marked Price (${\mathrm{MP}}_R$):

${\mathrm{MP}}_R={\mathrm{CP}}_R\times (1+0.20)=1.32x\times 1.20=1.584x$

4. Amount paid by Customer (Retailer's Selling Price):

$\text{Customer Price}={\mathrm{MP}}_R\times (1-0.08)=1.584x\times 0.92=1.45728x$

Step 3: Solve for $x$

We are given that the customer pays ₹12,216:

$1.45728x=12,216$

$x=\frac{12,216}{1.45728}\approx 8,382.74$

Rounding off to the nearest rupee, we get approximately ₹8,383.