Jacob bought a scooter and spent 10% of the cost price on repairs. He sold it for a profit of ₹1100, which represented a 20% profit on the total cost (including repairs). Determine the amount he spent on repairs.

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Accepted Answer

Let the original cost price (CP) of the scooter be ₹$$ x $$.

1. **Total cost including repairs:**  
   - Repair cost = $$10\% \, 	ext{of} \, x = 0.1x$$.  
   - Total CP = Original CP + Repairs = $$x + 0.1x = 1.1x$$.

2. **Calculate selling price (SP) based on 20% profit:**  
   - Profit = $$20\% \, 	ext{of total CP} = 0.2 	imes 1.1x = 0.22x$$.  
   - SP = Total CP + Profit = $$1.1x + 0.22x = 1.32x$$.

3. **Given profit amount is ₹1100:**  
   - Profit = SP - Total CP = $$1.32x - 1.1x = 0.22x$$.  
   - $$0.22x = 1100$$.  
   - Solve for $$ x $$:  
     $$
     x = \frac{1100}{0.22} = ₹5000.
     $$

4. **Calculate repair cost:**  
   - Repair cost = $$0.1x = 0.1 	imes 5000 = ₹500$$.

Thus, Jacob spent **₹500** on repairs.

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**Key Correction:**  
The profit percentage (20%) applies to the **total cost** (original CP + repairs), not the original CP alone. This ensures the correct calculation of $$ x $$ and the repair cost.

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