A person buys a certain number of oranges at ₹84 a dozen and two times of it at ₹72 a dozen. He sells all the oranges at ₹90 a dozen and makes a profit of ₹1680. How many oranges does he buy?

1440

Let the person buy 1 dozen orange at a Rs 84 a dozen and buy 2 dozen orange at 72 a dozen,

Cost of 1 dozen = 84

Cost of 2 dozen = 72 × 2 = 144

Total cost of 3 dozen = 144 + 84 = 228

SP of 1 dozen = 90

Total SP of 3 dozen = 90 × 3 = 270

Profit = 270 – 228 = 42

42 profit when buy = 3 dozen

1680 profit when buy = \(\frac{3}{42}\) × 1680 = 120 dozen

As we know,

1 dozen = 12

120 dozen = 120 × 12 = 1440