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?

Let the total cost of the raw materials purchased be $\text{₹}100$.
1. Calculate the cost of materials used and manufacturing cost:
* Wasted raw materials = $22.5\%\text{ of }100=\text{₹}22.5$
* Utilised raw materials = $100-22.5=\text{₹}77.5$
* Cost of manufacturing added = $80\%\text{ of }77.5=\frac{80}{100}\times 77.5=\text{₹}62$

2. Calculate the total investment/effective cost base:
* Total actual expenses incurred = Total raw materials purchased + Manufacturing cost
* $\text{Total Cost Incurred}=100+62=\text{₹}162$

3. **Calculate the Selling Price ($\text{SP}$):**
* Since he makes an overall profit of $20\%$:
* $\text{SP}=162\times \left(1+\frac{20}{100}\right)=162\times 1.2=\text{₹}194.4$

4. **Calculate the Marked Price ($\text{MP}$):**
* He sells the product at a $20\%$ discount on the marked price:
* $\text{SP}=\text{MP}\times \left(1-\frac{20}{100}\right)$
* $194.4=\text{MP}\times 0.8$
* $\text{MP}=\frac{194.4}{0.8}=\text{₹}243$

5. Find the required ratio:
* We need to find how many times the total cost of the raw materials purchased ($\text{₹}100$) is the marked price ($\text{₹}243$):
* $\text{Ratio}=\frac{\text{Marked Price}}{\text{Total Raw Material Cost}}=\frac{243}{100}=2.43\text{ times}$