saswata4s wrote:

A local grocer purchased eggs at a cost of c dollars per dozen each morning and sold all of them by the day end at a cost of s dollars per dozen. He made a profit of 100% on the sale of eggs each day. One morning there was a minor accident at the grocer’s shop in which some of the eggs he had bought that morning broke and therefore, were rendered unsaleable. The grocer sold the remaining eggs at their usual selling price and made a profit of 50% on the sale of eggs that day. What percentage of the eggs bought by the grocer that morning broke in the accident?

A) 25%

B) 33%

C) 50%

D) 67%

E) Cannot be determined

Let grocer bought and sold \(n\) dozens of egg.

As his profit is 100% implying \(s=2c\)

Total cost price \(= c*n\). let \(x\) eggs broke. So he sold \(n-x\) eggs

Total Selling price \(= (n-x)*2c\)

Hence profit%\(=\frac{(n-x)*2c-c*n}{c*n}=\frac{1}{2}\)

\(=>\frac{2cn-2cx-cn}{cn}=\frac{1}{2}=>\frac{n-x}{n}=\frac{1}{2}=>1-\frac{x}{n}=\frac{1}{2}\)

Therefore \(\frac{x}{n}=\frac{1}{2}=25\)%

Option

A----------------------------------------------------------------

Alternatively, you can also work through options.

Let he bought 100 dozen eggs. Using option A, he now has 75 dozen eggs

CP per dozen = c and SP per dozen=s=2c

so total cost=100c and total SP=2c*75=150c

Therefore profit %=(150c-100c)/100c=50%. Hence Option A is correct

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