when a plot is sold for rs. 18,700, the owner loses 15%. at what price must that plot be sold in order to gain 15%?
Here’s a friendly explanatory post styled as a “Quick Scoop” — detailed yet easy to follow 👇
When a Plot Is Sold for ₹18,700, the Owner Loses 15%. At What Price Must
That Plot Be Sold to Gain 15%?
🟡 Quick Scoop
Let’s crack this classic profit-and-loss puzzle that often appears in math exams — and even real-life property deals!
Step 1: Decode What’s Given
- Selling Price (SP₁) = ₹18,700
- Loss = 15%
We know that:
SP=CP×(1−Loss%100)SP=CP\times \left(1-\frac{Loss%}{100}\right)SP=CP×(1−100Loss%)
Substituting the given values:
18,700=CP×(1−15100)18,700=CP\times \left(1-\frac{15}{100}\right)18,700=CP×(1−10015)
18,700=CP×0.8518,700=CP\times 0.8518,700=CP×0.85
So,
CP=18,7000.85=₹22,000CP=\frac{18,700}{0.85}=₹22,000CP=0.8518,700=₹22,000
Step 2: Find New Selling Price for 15% Gain
Now the owner wants a 15% gain , so:
SP2=CP×(1+15100)SP₂=CP\times \left(1+\frac{15}{100}\right)SP2=CP×(1+10015)
SP2=22,000×1.15=₹25,300SP₂=22,000\times 1.15=₹25,300SP2=22,000×1.15=₹25,300
✅ Final Answer
When a plot is sold for ₹25,300 , the owner makes a 15% profit.
🧠 Quick Recap Table
| Condition | Loss/Gain % | Selling Price |
|---|---|---|
| Original (with loss) | -15% | ₹18,700 |
| Desired (with gain) | +15% | ₹25,300 |
