By selling an article for Rs 900, a man gains 20%. Find his cost price and the gain.

Answer

To solve the problem step by step, we will first find the cost price (CP) of the article and then calculate the gain.

### Step 1: Identify the given values
- Selling Price (SP) = Rs 900
- Gain percentage = 20%

### Step 2: Use the formula to find the Cost Price (CP)
The formula to calculate the Cost Price (CP) when the Selling Price (SP) and gain percentage are known is:

\[ CP = \frac{100}{100 + \text{gain percent}} \times SP \]

### Step 3: Substitute the values into the formula
Substituting the values we have:

\[ CP = \frac{100}{100 + 20} \times 900 \]

### Step 4: Simplify the equation
Now, simplify the equation:

\[ CP = \frac{100}{120} \times 900 \]

### Step 5: Calculate the fraction
Calculating the fraction:

\[ CP = \frac{5}{6} \times 900 \]

### Step 6: Perform the multiplication
Now, multiply:

\[ CP = 750 \]

So, the Cost Price (CP) is Rs 750.

### Step 7: Calculate the Gain
To find the gain, we can use the formula:

\[ \text{Gain} = SP - CP \]

Substituting the values we have:

\[ \text{Gain} = 900 - 750 \]

### Step 8: Perform the subtraction
Now, perform the subtraction:

\[ \text{Gain} = 150 \]

### Final Answer
- Cost Price (CP) = Rs 750
- Gain = Rs 150

---