Rohan bought a bike at 15% discount on MRP. After 1 year Rohan sold the bike to Gopal at 10% loss. After 1 more year Gopal sold the bike at 15% profit to Sumit . If sumit paid Rs. 1,40,000 then find the M.R.P. of the bike ?

Options

A. 1,59,000
B. 1,55,000
C. 1,40,000
D. 2,00,000

Explanation

To find the M.R.P. of the bike, we will follow these steps:

### Step 1: Determine the price Rohan bought the bike for after the discount.
Let the M.R.P. of the bike be \( x \).

Rohan bought the bike at a 15% discount. Therefore, the price Rohan paid is:
\[ \text{Price paid by Rohan} = x - 0.15x = 0.85x \]

### Step 2: Calculate the selling price when Rohan sold the bike to Gopal at a loss.
Rohan sold the bike to Gopal at a 10% loss. The selling price can be calculated as:
\[ \text{Selling price to Gopal} = \text{Price paid by Rohan} - 10\% \text{ of Price paid by Rohan} \]
\[ = 0.85x - 0.10(0.85x) = 0.85x - 0.085x = 0.765x \]

### Step 3: Calculate the selling price when Gopal sold the bike to Sumit at a profit.
Gopal sold the bike to Sumit at a 15% profit. The selling price can be calculated as:
\[ \text{Selling price to Sumit} = \text{Selling price to Gopal} + 15\% \text{ of Selling price to Gopal} \]
\[ = 0.765x + 0.15(0.765x) = 0.765x + 0.11475x = 0.87975x \]

### Step 4: Set the selling price to Sumit equal to Rs. 1,40,000.
According to the problem, Sumit paid Rs. 1,40,000 for the bike:
\[ 0.87975x = 140000 \]

### Step 5: Solve for the M.R.P. (x).
To find \( x \), we rearrange the equation:
\[ x = \frac{140000}{0.87975} \]
Calculating this gives:
\[ x \approx 159,000 \]

### Conclusion
The M.R.P. of the bike is approximately Rs. 1,59,000.

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