question_answer

A trader has 300 kg of rice, part of which he sells at 10% profit and the remaining quantity at 15% loss. On the whole, he incurs on overall loss of 5%. What is the quantity of rice that he sold at 15% loss?

A)  120 kg             

B)  100kg  

C)  160 kg 

D)         180kg  

E)         105kg

Correct Answer: D

Solution :

Suppose he sells x kg at 10% profit and the remaining pan (300 - x) kg at 15% loss. Now \[x\times \frac{110}{100}+(300-x)\times \frac{85}{100}=300\times \frac{95}{100}\] Or, \[\frac{11x}{10}-\frac{17x}{20}=285-255\] \[\frac{22x-17x}{20}=30\] Or, \[x=\frac{30\times 20}{5}=120kg\] The quantity he sells at 15% loss = (300 -120) = 180 kg By Allegation Method: Reqd quantity at 15% loss \[=\frac{300}{5}\times 3=180kg\]