Discussion
A grocer has 80 kg rice, a part of which he sells at 8% profit and the rest at 18% profit. He gains 14% on the whole. What is the quantity of rice sold at 18% profit ?
Answer: D
The quantity sold at 18% profit is 48 kg.
By alligation, the two parts are in the ratio of the differences from the average profit of 14%:
\[ \begin{aligned} 8\% : 18\% &= (18 - 14) : (14 - 8) \\ &= 4 : 6 = 2 : 3 \\ \text{at } 18\% &= \tfrac{3}{5} \times 80 = 48 \end{aligned} \]
Check: 32 kg at 8% and 48 kg at 18% give an average of \(\frac{32 \times 8 + 48 \times 18}{80} = 14\%\). 32 kg is the part sold at 8%, which is the trap.
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