Nalini purchased 20 dozen of apples at ₹48 per dozen. She sold 8 dozen of them at 10% profit and the remaining 12 dozen at 20% profit. What is the overall profit percentage gained in this transaction?

Nalini purchased 20 dozen of apples at ₹48 per dozen.

Cost price of 20 dozen of apples = ₹48 $$\times$$ 20 = ₹960   Eq.(i)

She sold 8 dozen of them at 10% profit.

Selling price of 8 dozen of apples = ₹48 of (100+10)% $$\times$$ 8

= ₹48 of 110% $$\times$$ 8

= $$48\times\frac{110}{100}\times8$$

= ₹422.4    Eq.(ii)

the remaining 12 dozen at 20% profit.

Selling price of remaining 12 dozen of apples = ₹48 of (100+20)% $$\times$$ 12

= 48 of 120% $$\times$$ 12

= $$48\times\frac{120}{100}\times12$$

Overall profit percentage gained in this transaction = $$\frac{\left(Eq.(ii)+Eq.(iii)\right)-Eq.(i)}{Eq.(i)}\times\ 100$$

= $$\frac{\left(422.4+691.2\right)-960}{960}\times\ 100$$

= $$\frac{1113.6-960}{960}\times\ 100$$

= $$\frac{153.6}{960}\times\ 100$$

= $$\frac{1536}{96}$$

= 16%