Due to economic surges the price of eggs suddenly reduced by 40%. This enabled…

Concept

When a price falls, the same money buys more units. If the original price per unit is P and it drops by a fraction r, the new price is (1 − r)·P. The number of units bought for a fixed amount M is M divided by the price, so the extra units gained equal M/[(1 − r)P] − M/P. Setting this gap equal to the given extra count yields one equation in P.

Application

1. Let the original price per egg be P. A 40% fall means the reduced price is 0.6P.

2. Eggs bought at the old price for $50 = 50/P; at the new price = 50/(0.6P).

3. Extra eggs = 50/(0.6P) − 50/P = (50/P)(1/0.6 − 1) = (50/P)(5/3 − 1) = (50/P)(2/3) = 100/(3P).

4. This extra equals 64, so 100/(3P) = 64 → P = 100/192 = $25/48 per egg.

5. Reduced price per egg = 0.6P = 0.6 × 25/48 = 5/16 = $0.3125.

6. Reduced price per dozen = 12 × 0.3125 = $3.75.

Cross-check

At the old price, $50 buys 50 ÷ (25/48) = 96 eggs; at the reduced price, $50 buys 50 ÷ (5/16) = 160 eggs. The difference is 160 − 96 = 64 eggs, exactly as stated, confirming the reduced price of $3.75 per dozen.