Question

A dealer has 1000 kg sugar, and he sells a part of it at 8% profit and the rest of it at 18% profit. The overall profit he earns is 14%. What is the quantity that is sold at 18% profit? 
 

• A. 450 kg
• B. 900 kg
• C. 630 kg
• D. 400 kg
• E. 600 kg

Hint:

Alligation is the fastest method for mixture and profit percentage problems.

Answer 1

Answer: (E)

Step 1: Using Alligation Method:
Let quantity sold at 18% profit be \(x\) kg, and at 8% profit be \((1000 - x)\) kg.
Overall profit = 14%.
Alligation:
Difference from overall:
18% - 14% = 4%
14% - 8% = 6%
Ratio of quantities (8% profit : 18% profit) = 4 : 6 = 2 : 3.

Step 2: Calculating Quantity:
Total parts = 2 + 3 = 5.
Quantity at 18% = \(\frac{3}{5} \times 1000 = 600\) kg.