A trader bought 640 kg of rice. He sold a part of the rice at 20% profit and the rest of 5% loss. He earned a profit of 15% in the entire transaction. What is the ratio of the quantity of rice that he sold at a loss of 5% to that of the quantity that he sold at a profit of 20%?

Let the part sold at 5% loss be = a kg
a × -5% + (640 - a) × 20% = 640 × $$\frac{{15}}{{100}}$$
⇒ -5a + 640 × 20 - 20a = 640 × 15
⇒ 640 × 20 - 640 × 15 = 25a
⇒ 640 × $$\frac{{\left( {20 - 15} \right)}}{{25}}$$  = a
⇒ a = 128 = Loss portion
So, Profit portion = 640 - 128
⇒ 512
Ratio = 128 : 512
⇒ 1 : 4
∴ Required ratio is 1 : 4