Question

A cook went to a market to buy some eggs and paid $12. But since the eggs were quite small, he talked the seller into adding two more eggs, free of charge. As the two eggs were added, the price per dozen went down by a dollar. How many eggs did the cook bring home from the market?
A. 8
B. 12
C. 15
D. 16
E. 18

Answer 1

Answer:

The correct answer is E that is 18 eggs.

Explanation:

Assuming initially eggs be n which he bought

So, the price per dozen = $(12×12/n)

But finally, he bought (n + 2) eggs in the same price that is $12.

So, the new price per dozen = $(12×12/(n + 2))

Therefore,

12×12/n - 12×12/(n + 2) = 1

Taking 12 × 12 common from the above equation:

(12×12)[(n + 2) - n]/[n(n + 2)] = 1

144×2 = n(n + 2)

n(n + 2) = 288

n² +2n - 288 = 0

Now, we can either solve the above quadratic equation as follows,

n² + 2n - 288 = 0

n² + 18n - 16n - 288 = 0

(n + 18)(n - 16) = 0

As n would be positive because eggs cannot be in negative numbers therefore, n = 16

And he bought 2 extra, So

n = 16 + 2

n = 18 eggs

The eggs he bought is 18