John sold an article to Peter at 20% profit and Peter sold it to Mohan at 5% loss. If Mohan paid Rs 912 for the article, find how much did John pay for it ?

Answer

To solve the problem step by step, we need to find out how much John paid for the article (CP1) given that Mohan paid Rs 912 for it after a series of transactions.

### Step 1: Understand the Transactions
- John sells the article to Peter at a 20% profit.
- Peter sells the article to Mohan at a 5% loss.
- Mohan pays Rs 912 for the article.

### Step 2: Determine Selling Price of Peter (SP2)
Since Mohan paid Rs 912, this amount is the selling price of Peter (SP2).
- SP2 = Rs 912

### Step 3: Calculate Cost Price for Peter (CP2)
Peter sold the article at a 5% loss. We can use the formula for selling price with loss:
\[ SP = CP - \text{Loss} \]
Where Loss = 5% of CP2.

Rearranging the formula gives us:
\[ SP2 = CP2 - (0.05 \times CP2) \]
\[ SP2 = CP2 \times (1 - 0.05) \]
\[ SP2 = CP2 \times 0.95 \]

Now substituting SP2:
\[ 912 = CP2 \times 0.95 \]

To find CP2:
\[ CP2 = \frac{912}{0.95} \]
\[ CP2 = 960 \]

### Step 4: Determine Selling Price of John (SP1)
Since Peter's cost price (CP2) is Rs 960, this amount is also the selling price for John (SP1):
- SP1 = Rs 960

### Step 5: Calculate Cost Price for John (CP1)
John sold the article to Peter at a 20% profit. We can use the formula for selling price with profit:
\[ SP = CP + \text{Profit} \]
Where Profit = 20% of CP1.

Rearranging the formula gives us:
\[ SP1 = CP1 + (0.2 \times CP1) \]
\[ SP1 = CP1 \times (1 + 0.2) \]
\[ SP1 = CP1 \times 1.2 \]

Now substituting SP1:
\[ 960 = CP1 \times 1.2 \]

To find CP1:
\[ CP1 = \frac{960}{1.2} \]
\[ CP1 = 800 \]

### Conclusion
Therefore, John paid Rs 800 for the article.

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