Due to an increase of 30% in the price of eggs, 3 eggs less are available for ₹ 7.80. The present rate of eggs per dozen is

### Concept & Formula When the price increases, the extra cost that would have been incurred to buy the original quantity equals the current cost of the missing quantity. ### Step-by-Step Solution * **Given:** Price increase = $30\%$, Quantity reduced = $3$ eggs, Total amount = ₹ $7.80$. * **Calculation:** If the person wanted to buy the exact same number of eggs as before, they would need $30\%$ more money. Extra money required = $30\%$ of $7.80$ Extra money = $0.30 \times 7.80 = 2.34$ Since they didn't spend this extra ₹ $2.34$, they received $3$ eggs less. This means ₹ $2.34$ represents the cost of those $3$ missing eggs at the *present* (increased) rate. Present price of $1$ egg = $\frac{2.34}{3} = $ ₹ $0.78$ The question asks for the rate per dozen ($12$ eggs): Present price per dozen = $0.78 \times 12$ Present price per dozen = ₹ $9.36$ ### Exam Strategy & Shortcut You can jump straight to the new price per unit using the direct shortcut formula: $$ \text{New Price} = \frac{\text{Percentage Change} \times \text{Total Amount}}{100 \times \text{Change in Quantity}} $$ New Price of $1$ egg = $\frac{30 \times 7.80}{100 \times 3} = \frac{234}{300} = 0.78$ Don't forget the final step! Multiply by $12$ for a dozen: $0.78 \times 12 = 9.36$. ### Common Pitfall Forgetting to multiply the final single-unit price by 12. Students often correctly calculate the price of a single egg ($0.78$) and then get confused when it's not in the options, or worse, if a trap option matches a single unit calculation. Always re-read the final unit requested! ### Final Answer Therefore, the correct answer is **₹ 9.36**.