Question

A man purchased some eggs at 3 for RS 16 per dozen and sold them at 5 for RS 36. Thus, he gained RS 168 in all . how many eggs did he purchased

Answer 1

Let total eggs be x

Cost Price of 3 eggs = 16

Cost Price of 1 egg = 16/3

Cost Price of x eggs = 16x/3

Selling price of 5 eggs = 36

Selling price of 1 egg = 36/5

Selling price of x eggs = 36x/5

Profit = SP - CP

= 36x/5 - 16x/3

= (108x - 80x) / 15

= 28x/15

So, 28x/15 = 168

x = 2520/28

x = 90

So he purchased 90 eggs.

Answer 2

$given \: cp \: of \: 3eggs = 16 \\ cp \: of \: x \: eggs = \frac{16}{3x} \\ \\ sp \: of \: 5 \: eggs \: = 12 \\ sp \: of \: x \: eggs \: = \frac{36}{5x} \\ so \\ profit = sp - cp \\ 168 = \frac{36x}{5} - \frac{16}{3x} \\ 168 = \frac{108x}{15} - \frac{80x}{15} \\ transpose \: the \: values \\ \frac{28x}{15} = 168 \\ 168 \times 15 = 28x \\ 2520 = 18x \\ x = \frac{2520}{28} \\ x = 90$