Price rise and quantity drop — eggs per dozen after a 30% increase Due to a 30% increase in the price of eggs, a buyer gets 3 fewer eggs for Rs 7.80 than before. What is the present price per dozen?

Introduction / Context:When price increases by a known percent, the affordable quantity for a fixed amount of money falls in inverse proportion. By comparing the two quantities, we can recover the original unit price and hence the new price per dozen after the 30% rise.

Given Data / Assumptions:

• Money available = Rs 7.80 (fixed).
• New price = 1.30 × old price per egg.
• Quantity difference = 3 eggs fewer after the increase.

Concept / Approach:If the original count was q = 7.80/old_price, the new count is q/1.30. The given difference q − q/1.30 = 3 allows solving for q and, in turn, both old and new unit prices.

Step-by-Step Solution:q − q/1.30 = 3 ⇒ q(1 − 1/1.30) = 3 ⇒ q × (0.30/1.30) = 3.q = 3 × 1.30 / 0.30 = 13 eggs (originally).Old price per egg = 7.80 / 13 = Rs 0.60.New price per egg = 1.30 × 0.60 = Rs 0.78.Present rate per dozen = 12 × 0.78 = Rs 9.36.

Verification / Alternative check:Originally 13 eggs for 7.80; now 7.80/0.78 = 10 eggs ⇒ 3 fewer, as stated.

Why Other Options Are Wrong:Rs 8.64 and 8.88 correspond to different percentage changes; 'None of these' is false; Rs 9.00 does not fit the 30% rise math.

Common Pitfalls:Applying 30% to the number of eggs rather than to price, or mixing rupees and paise in the arithmetic.

Final Answer:Rs 9.36