Rajesh sold his scooter to Rahim at 8% loss and Rahim, in turn, sold the same scooter to Prem at 5% gain. If Prem paid Rs 14,490 for the scooter, find :
the S.P. and the C.P. of the scooter for Rajesh.

Answer

To solve the problem step by step, we will find the selling price (SP) and cost price (CP) of the scooter for Rajesh.

### Step 1: Understand the relationships between the prices
- Rajesh sold the scooter to Rahim at an 8% loss.
- Rahim sold the scooter to Prem at a 5% gain.
- Prem paid Rs 14,490 for the scooter.

### Step 2: Find the cost price for Rahim (CP2)
Let’s denote:
- CP2 = Cost Price for Rahim
- SP2 = Selling Price for Rahim (which is equal to the price Prem paid)

From the problem, we know:
- SP2 = Rs 14,490
- Rahim sold the scooter at a 5% gain.

Using the formula for selling price:
\[ SP2 = CP2 + \text{Gain} \]
\[ \text{Gain} = 5\% \text{ of } CP2 = 0.05 \times CP2 \]

Thus, we can write:
\[ SP2 = CP2 + 0.05 \times CP2 \]
\[ SP2 = CP2 \times (1 + 0.05) \]
\[ SP2 = CP2 \times 1.05 \]

Now substituting the value of SP2:
\[ 14,490 = CP2 \times 1.05 \]

To find CP2, we rearrange the equation:
\[ CP2 = \frac{14,490}{1.05} \]

Calculating CP2:
\[ CP2 = \frac{14,490}{1.05} = 13,800 \]

### Step 3: Find the selling price for Rajesh (SP1)
Since SP1 (selling price for Rajesh) is equal to CP2 (cost price for Rahim):
\[ SP1 = CP2 = 13,800 \]

### Step 4: Find the cost price for Rajesh (CP1)
Rajesh sold the scooter at an 8% loss. We can express this as:
\[ SP1 = CP1 - \text{Loss} \]
\[ \text{Loss} = 8\% \text{ of } CP1 = 0.08 \times CP1 \]

Thus, we can write:
\[ SP1 = CP1 - 0.08 \times CP1 \]
\[ SP1 = CP1 \times (1 - 0.08) \]
\[ SP1 = CP1 \times 0.92 \]

Now substituting the value of SP1:
\[ 13,800 = CP1 \times 0.92 \]

To find CP1, we rearrange the equation:
\[ CP1 = \frac{13,800}{0.92} \]

Calculating CP1:
\[ CP1 = \frac{13,800}{0.92} = 15,000 \]

### Final Answers
- Selling Price for Rajesh (SP1) = Rs 13,800
- Cost Price for Rajesh (CP1) = Rs 15,000