Ramanna purchased raw materials for a certain price to manufacture a product. However, owing to shortage of labour, 22.5% of the raw materials could not be utilised and got wasted. 80% of the cost of raw materials used was added as the cost of manufacturing. If Ramanna could sell his product at a price to earn an overall profit of 20% after offering a discount of 20%, how many times of the total cost of the raw materials purchased was the marked price of the product?

The correct option is 2.43 times.

Let us assume that the total cost of raw materials purchased by Ramanna is 100 units.

Step 1: Calculate the cost of raw materials used
Owing to a shortage of labor, 22.5% of the raw materials could not be utilized and got wasted.

Percentage of raw materials utilized = 100% - 22.5% = 77.5%

Therefore, the cost of raw materials used is:

$\text{Cost of raw materials used}=77.5$

Step 2: Calculate the manufacturing cost
It is given that 80% of the cost of raw materials used was added as the cost of manufacturing.

$\text{Manufacturing cost}=80\%\text{of}77.5=0.80\times 77.5=62$

Step 3: Calculate the total cost price (CP) of the product
The total cost price incurred by Ramanna includes the cost of raw materials purchased plus the manufacturing cost:

$\text{Total CP}=100+62=162$

Step 4: Calculate the selling price (SP) of the product
Ramanna earns an overall profit of 20% on the total cost price.

$\text{Selling Price (SP)}=\text{CP}\times (1+0.20)=162\times 1.20=194.4$

Step 5: Calculate the marked price (MP) of the product
The product was sold after offering a discount of 20% on the marked price.

$\text{Selling Price (SP)}=\text{MP}\times (1-0.20)=0.80\times \text{MP}$

Equating the selling price expressions:

$0.80\times \text{MP}=194.4$

$\text{MP}=\frac{194.4}{0.80}=243$

Step 6: Determine the ratio of Marked Price to the total cost of raw materials purchased

$\text{Ratio}=\frac{\text{Marked Price}}{\text{Total Cost of Raw Materials Purchased}}=\frac{243}{100}=2.43$

Thus, the marked price of the product was 2.43 times the total cost of the raw materials purchased.