Selling rate for a rice mixture — Aptitude Question
Selling rate for a rice mixture: A grocer buys 80 kg of rice at ₹13.50 per kg and mixes it with 120 kg at ₹16 per kg. Answer and worked solution on CodeKairo.
- Topic: Profit & Loss
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 90 seconds
Question
A grocer buys 80 kg of rice at ₹13.50 per kg and mixes it with 120 kg at ₹16 per kg. At what rate per kg must he sell the mixture to gain 16%?
Options
- ₹16.50
- ₹17.00
- ₹17.40
- ₹18.00
Show the answer and the worked solution
Correct answer: C. ₹17.40
Worked solution
- Cost = 80 × 13.50 + 120 × 16 = 1,080 + 1,920 = ₹3,000.
- For a 16% gain, total SP = 3,000 × 1.16 = ₹3,480.
- Rate = 3,480 ÷ 200 = ₹17.40 per kg.
Answer: ₹17.40.
The idea
Total the cost, apply the profit to the total, then divide by the total quantity. Averaging the two buying rates first is wrong whenever the quantities differ.
Shortcut. The 200 kg cost a round ₹3,000, i.e. ₹15 a kg; adding 16% gives 15 × 1.16 = ₹17.40.
Common trap. "₹17.00" — averaging the two buying rates, (13.50 + 16) ÷ 2 = 14.75, then adding 16% gives about 17.11; the 120 kg at ₹16 should weigh more.