A consignment sold in two parts — Aptitude Question
A consignment sold in two parts: Two-thirds of a consignment was sold at a 5% profit and the rest at a 2% loss,… Answer and worked solution on CodeKairo.
- Topic: Profit & Loss
- Section: Quantitative Aptitude
- Difficulty: Hard
- Time target: 120 seconds
Question
Two-thirds of a consignment was sold at a 5% profit and the rest at a 2% loss, giving an overall profit of ₹400. What was the value of the consignment?
Options
- ₹12,000
- ₹15,000
- ₹18,000
- ₹20,000
Show the answer and the worked solution
Correct answer: B. ₹15,000
Worked solution
- Profit on two-thirds = (2/3)x × 0.05 = x/30.
- Loss on one-third = (1/3)x × 0.02 = x/150.
- Net = x/30 − x/150 = (5x − x)/150 = 4x/150 = 2x/75.
- 2x/75 = 400 → x = ₹15,000.
Answer: ₹15,000.
The idea
Weight each rate by the fraction of stock it applies to, subtract, and solve. Working in fractions rather than decimals keeps the arithmetic exact.
Shortcut. Net rate = (2/3 × 5) − (1/3 × 2) = (10 − 2)/3 = 8/3 % of the value, so the value is 400 × 300/8 = ₹15,000.
Common trap. "₹12,000" — counting only the 5% profit on two-thirds (10/3 % of the value) and forgetting to subtract the loss on the other third.