Previously, the manufacturing cost of a product was thrice the cost of raw material. Now the cost of raw material increases in the ratio 5 : 12 and manufacturing cost increases in the ratio of 3 : 5. The previous cost of the product was ₹ 8. What should be the present selling price so that 25% profit can be made? (Hotel Management, 2007)

### Concept & Proportional Changes The total cost of a product is the sum of its raw material and manufacturing costs. By using the given initial ratios and total cost, we can find the exact initial values. Ratios of increase are then applied to find the new total cost before calculating the final selling price for a desired profit margin. $$ \text{Total Cost} = \text{Raw Material Cost} + \text{Manufacturing Cost} $$ $$ \text{Selling Price} = \text{Total Cost} \times \left(1 + \frac{\text{Profit \%}}{100}\right) $$ ### Step-by-Step Solution * Let the initial cost of raw material be $R$ and manufacturing cost be $M$. * Given that manufacturing cost was thrice the raw material cost: $M = 3R$. * Total previous cost = $R + M = R + 3R = 4R$. * We are given the previous total cost was ₹ 8. So, $4R = 8 \implies R = 2$. * Therefore, initial raw material cost $R = 2$ and initial manufacturing cost $M = 6$. * The raw material cost increases in the ratio $5 : 12$. New raw material cost = $2 \times \frac{12}{5} = \frac{24}{5} = 4.8$. * The manufacturing cost increases in the ratio $3 : 5$. New manufacturing cost = $6 \times \frac{5}{3} = 10$. * Present total cost = New $R$ + New $M = 4.8 + 10 = 14.8$. * Desired profit is $25\%$. * Present selling price = $14.8 \times \left(1 + \frac{25}{100}\right) = 14.8 \times 1.25 = 18.5$. ### Exam Strategy & Shortcut Break the ₹ 8 into a $1:3$ ratio mentally ($₹ 2$ and $₹ 6$). A $5:12$ ratio increase means the new value is $\frac{12}{5}$ of the old. $2 \times 2.4 = 4.8$. A $3:5$ increase means multiplying by $\frac{5}{3}$. $6 \times \frac{5}{3} = 10$. Total cost is $14.8$. Adding $25\%$ ($\frac{1}{4}$) to $14.8$: $\frac{14.8}{4} = 3.7$. $14.8 + 3.7 = 18.5$. ### Common Pitfall A frequent error is interpreting "increases in the ratio a : b" as adding a fraction, rather than seeing it as the multiplier $\frac{b}{a}$ where $a$ represents the old value and $b$ represents the new value. ### Final Answer Therefore, the correct answer is **₹ 18.50**.