Rohit sold his car at 10% below the cost price to Amit. Amit got the car repaired and spent Rs. 5,000. He then sold the car to Rajesh at 20% above the total cost, which is equal to Rs. 1,00,000. Find the original price of the car (nearest to hundred).

Options

A. Rs. 93,000
B. Rs. 83,000
C. Rs. 87,000
D. Rs. 97,000

Answer

To find the original price of the car, we can break down the problem into a series of steps.

### Step-by-Step Solution:

1. **Define the Cost Price (CP)**:
Let the original cost price of the car be \( CP \).

2. **Calculate the Selling Price to Amit**:
Rohit sold the car at 10% below the cost price. Therefore, the selling price (SP) to Amit is:
\[ SP_{Amit} = CP - 0.10 \times CP = 0.90 \times CP \]

3. **Amit's Total Cost**:
Amit spent Rs. 5,000 on repairs. Thus, his total cost (TC) for the car is:
\[ TC_{Amit} = SP_{Amit} + 5000 = 0.90 \times CP + 5000 \]

4. **Selling Price to Rajesh**:
Amit sold the car to Rajesh at 20% above his total cost. Therefore, the selling price (SP) to Rajesh is:
\[ SP_{Rajesh} = TC_{Amit} + 0.20 \times TC_{Amit} = 1.20 \times TC_{Amit} \]

5. **Setting the Selling Price to Rajesh**:
We know that Amit sold the car to Rajesh for Rs. 1,00,000. So we can set up the equation:
\[ 1.20 \times TC_{Amit} = 100000 \]

6. **Substituting for TC_Amit**:
Substitute \( TC_{Amit} \) from step 3 into the equation:
\[ 1.20 \times (0.90 \times CP + 5000) = 100000 \]

7. **Distributing and Solving the Equation**:
Expanding the left side:
\[ 1.08 \times CP + 6000 = 100000 \]
Now, subtract 6000 from both sides:
\[ 1.08 \times CP = 100000 - 6000 = 94000 \]

8. **Finding the Cost Price (CP)**:
Divide both sides by 1.08 to find \( CP \):
\[ CP = \frac{94000}{1.08} \approx 87037.04 \]

9. **Rounding to the Nearest Hundred**:
Rounding \( CP \) to the nearest hundred gives us:
\[ CP \approx 87000 \]

### Final Answer:
The original price of the car is approximately **Rs. 87,000**.