4 kg of sugar costing Rs 50 per kg is mixed with 8 kg of sugar costing Rs 60 per kg. At what price per kg should the mixture be sold to gain a profit of 20%?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → Rs 68 per kg
The profit is added to the average cost of the mixture, so the total cost is shared over the total weight first.
Total cost \(=4\times50+8\times60=200+480=\) Rs 680
Total weight \(=4+8=12\) kg
Cost per kg \(\displaystyle =\frac{680}{12}=\frac{170}{3}\)
Selling price \(\displaystyle =\frac{170}{3}\times\frac{120}{100}=68\)
The mixture must be sold at Rs 68 per kg.
Why the other options are incorrect
Option (1) Rs 56.6 per kg — Incorrect. This is about the cost price of the mixture, before the profit is added.
Option (2) Rs 64 per kg — Incorrect. It is 20% above Rs 53.33, which is not the average cost of the mixture.
Option (4) Rs 72 per kg — Incorrect. It is 20% above Rs 60, the cost of the dearer sugar alone.