The cost of $16$ packets of salt, each weighing $900$ grams is ₹ $28$. What will be the cost of $27$ packets, if each packet weighs $1$ kg?

### Concept & Chain Rule The total cost of goods is directly proportional to the total weight of the goods (number of items multiplied by the weight per item). $$ \frac{\text{Cost}_1}{N_1 \times W_1} = \frac{\text{Cost}_2}{N_2 \times W_2} $$ ### Step-by-Step Solution * **Given**: - Case 1: $N_1 = 16$, $W_1 = 900$ g, $\text{Cost}_1 = 28$ - Case 2: $N_2 = 27$, $W_2 = 1000$ g (converted from 1 kg), $\text{Cost}_2 = x$ * **Calculation**: $$ \frac{28}{16 \times 900} = \frac{x}{27 \times 1000} $$ Simplify the denominators: $$ \frac{28}{14400} = \frac{x}{27000} $$ Solve for $x$: $$ x = \frac{28 \times 27000}{14400} = \frac{28 \times 270}{144} $$ $$ x = 28 \times \frac{15}{8} = 7 \times \frac{15}{2} = \frac{105}{2} = 52.50 $$ ### Exam Strategy & Shortcut Compare the multipliers. Quantity goes from $16$ to $27$ (factor of $\frac{27}{16}$). Weight goes from $900$ to $1000$ (factor of $\frac{10}{9}$). New cost = $28 \times \frac{27}{16} \times \frac{10}{9} = 28 \times \frac{3}{16} \times 10 = \frac{840}{16} = 52.50$. ### Common Pitfall Forgetting to convert $1$ kg to $1000$ grams, resulting in a severe mismatch of units and an incorrect decimal answer. ### Final Answer Therefore, the correct answer is **₹ 52.50**.