A sells some articles to B at a gain of `20%`, while B to C at `25%` gain. If C pays Rs.975/-.How much did A pay for it?

Answer

To solve the problem step by step, we will follow the transactions between A, B, and C, and calculate the cost price that A paid for the articles.

### Step 1: Define the Cost Price
Let the cost price of the article for A be Rs. X.

**Hint:** Start by defining the variable for the cost price to make calculations easier.

### Step 2: Calculate Selling Price from A to B
A sells the article to B at a gain of 20%.
The selling price (SP) from A to B can be calculated as:
\[ SP_{A \to B} = X + 20\% \text{ of } X = X + \frac{20}{100} \times X = \frac{120}{100} \times X = \frac{120X}{100} \]
Thus,
\[ SP_{A \to B} = \frac{120X}{100} = 1.2X \]

**Hint:** Remember that selling price is calculated by adding the profit percentage to the cost price.

### Step 3: Calculate Selling Price from B to C
B sells the article to C at a gain of 25%.
Now, the selling price from B to C can be calculated as:
\[ SP_{B \to C} = SP_{A \to B} + 25\% \text{ of } SP_{A \to B} \]
Substituting the value from Step 2:
\[ SP_{B \to C} = 1.2X + \frac{25}{100} \times 1.2X = 1.2X + 0.25 \times 1.2X = 1.2X \times \left(1 + 0.25\right) = 1.2X \times 1.25 \]
Thus,
\[ SP_{B \to C} = \frac{1.2 \times 1.25X}{1} = \frac{150X}{100} = 1.5X \]

**Hint:** When calculating the new selling price, remember to multiply the previous selling price by (1 + profit percentage).

### Step 4: Set Up the Equation
According to the problem, C pays Rs. 975 for the article. Therefore, we can set up the equation:
\[ 1.5X = 975 \]

**Hint:** Equate the selling price to the amount paid by C to find the cost price.

### Step 5: Solve for X
To find the cost price X, we solve the equation:
\[ X = \frac{975}{1.5} \]
Calculating this gives:
\[ X = 650 \]

**Hint:** When dividing, ensure you perform the calculation accurately to find the value of X.

### Conclusion
Thus, the cost price that A paid for the article is Rs. 650.

**Final Answer:** A paid Rs. 650 for the article.