5 kg of superior quality rice is mixed with 25 kg of inferior quality rice. The prices of the superior and inferior quality rice are Rs 18 per kg and Rs 12 per kg respectively. What is the average price (in Rs per kg) of the mixture?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 13
The average price is the total cost divided by the total weight, not the simple average of the two prices.
Total cost \(=5\times18+25\times12=90+300=\) Rs 390
Total weight \(=5+25=30\) kg
Average price \(\displaystyle =\frac{390}{30}=13\)
The mixture costs Rs 13 per kg.
Why the other options are incorrect
Option (1) 15 — Incorrect. It is the simple average of 18 and 12, which would hold only for equal weights.
Option (2) 14 — Incorrect. It would need the superior and inferior rice in the ratio 1 : 2, not 5 : 25.
Option (4) 16 — Incorrect. It lies nearer the superior price, though most of the mixture is the cheaper rice.