Question : A trader bought 640 kg of rice. He sold a part of the rice at a 20% profit and the rest at a 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%?
Option 1: 1 : 3
Option 2: 4 : 1
Option 3: 1 : 4
Option 4: 3 : 1
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Correct Answer: 1 : 4
Solution :
Let the part of rice sold at a 5% loss as 'a' kg and the rest of the rice (640 – a) kg is sold at a 20% profit.
The overall profit from the entire transaction is 15%.
$⇒a \times -5\% + (640 - a) \times 20\% = 640 \times 15\%$
$⇒-a \times 0.05+(640-a)\times0.2=640 \times0.15$
$⇒-0.25a + 128= 96$
$⇒ 0.25a=32$
$⇒a = 128$
Therefore, the quantity of rice sold at a 20% profit = 640 – 128 = 512 kg
The ratio of the quantity of rice sold at a 5% loss to that sold at a 20% profit = 128 : 512 = 1 : 4
Hence, the correct answer is 1 : 4.
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