percentage and consumption arithmetic

Question

Due to an increment of 50% in the price of egg a person is able to buy 4 eggs less for Rs. 24. Find the initial cost of per dozen egg?

I am getting the answer as 24. However, the answer given in the book is 36. Please help regarding this.

Answer 1

Let :

$p$ = unit price of egg,

$n$ = number of eggs.

1) $p \times n =24$ --- before increase of price

2) $1.5 p \times (n-4) = 24$ --- after increase of price.

It seems that the answer provided in the book is wrong...

$36$ must be the cost per dozen after the price increase.

Answer 2

HINTS

Let $n_b,n_a$ denote the amounts (before and after) of the eggs you could get for Rs. $24$, and $p_b,p_a$ denote the likewise prices. Then $$ p_b n_b = 24 = p_a n_a $$ and you also have the constraints $$ p_a = 1.5 p_b \quad \text{and} \quad n_a = n_b-4 \ge 1. $$

Can you solve this now?