Had he bought cheaper — Profit & Loss Aptitude Question
Had he bought cheaper: A man sells an article at a profit of 10%. Had he bought it for 10% less and sold it for ₹35… Answer and worked solution on CodeKairo.
- Topic: Profit & Loss
- Section: Quantitative Aptitude
- Difficulty: Hard
- Time target: 135 seconds
Question
A man sells an article at a profit of 10%. Had he bought it for 10% less and sold it for ₹35 less, he would have gained 20%. What was the cost price?
Options
- ₹1,250
- ₹1,400
- ₹1,750
- ₹2,000
Show the answer and the worked solution
Correct answer: C. ₹1,750
Worked solution
- Let CP = x. Original SP = 1.1x.
- New CP = 0.9x, and a 20% gain on it means SP = 1.2 × 0.9x = 1.08x.
- That new SP is also 1.1x − 35, so 1.1x − 35 = 1.08x.
- 0.02x = 35 → x = ₹1,750.
Answer: ₹1,750.
The idea
Express every quantity as a multiple of the unknown cost, then set the two expressions for the new selling price equal. The small coefficient (0.02) is why the answer is large.
Shortcut. The ₹35 is the gap between the two selling prices: 110% of CP versus 120% of 90% = 108% of CP. So 2% of CP = ₹35 and CP = 35 × 50 = ₹1,750.
Common trap. "₹2,000" — the tempting round figure; check it: SP 2,200 at 10% profit, new cost 1,800 sold at 20% for 2,160, a gap of ₹40, not ₹35.