A shopkeeper has two articles A & B. He sold A at Rs 128 and cost price of article A is Rs x and gains (x - 20)% in this transaction. If cost price of article B is 25% more than A, then find at what price shopkeeper should sold B to make of profit of 40%?

Options

A. 118
B. 124
C. 136
D. 140

Answer

To solve the problem step by step, we will follow the details provided in the question and the video transcript.

### Step 1: Understand the Selling Price and Cost Price of Article A
The selling price (SP) of article A is given as Rs 128. The cost price (CP) of article A is Rs x. The profit percentage is given as (x - 20)%.

### Step 2: Set Up the Profit Equation
The profit can be calculated using the formula:
\[ \text{Profit} = \text{Selling Price} - \text{Cost Price} \]
We can also express profit in terms of percentage:
\[ \text{Profit} = \frac{\text{Profit Percentage}}{100} \times \text{Cost Price} \]

From the problem, we can write:
\[ \text{Profit} = 128 - x \]
And the profit percentage is:
\[ \frac{x - 20}{100} \times x \]

Setting these two expressions for profit equal gives us:
\[ 128 - x = \frac{x - 20}{100} \times x \]

### Step 3: Solve the Equation
Multiply both sides by 100 to eliminate the fraction:
\[ 100(128 - x) = (x - 20)x \]
Expanding both sides:
\[ 12800 - 100x = x^2 - 20x \]
Rearranging gives us a quadratic equation:
\[ x^2 + 80x - 12800 = 0 \]

### Step 4: Use the Quadratic Formula
The quadratic formula is given by:
\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
Here, \( a = 1, b = 80, c = -12800 \).

Calculating the discriminant:
\[ b^2 - 4ac = 80^2 - 4 \times 1 \times (-12800) = 6400 + 51200 = 57600 \]

Now, applying the quadratic formula:
\[ x = \frac{-80 \pm \sqrt{57600}}{2 \times 1} \]
\[ x = \frac{-80 \pm 240}{2} \]

Calculating the two possible values for x:
1. \( x = \frac{160}{2} = 80 \)
2. \( x = \frac{-320}{2} = -160 \) (not valid since cost price cannot be negative)

Thus, the cost price of article A is:
\[ x = 80 \]

### Step 5: Calculate the Cost Price of Article B
The cost price of article B is 25% more than that of article A:
\[ \text{CP of B} = x + 0.25x = 1.25x = 1.25 \times 80 = 100 \]

### Step 6: Determine the Selling Price of Article B for 40% Profit
To find the selling price for a 40% profit on article B:
\[ \text{Selling Price} = \text{Cost Price} + \text{Profit} \]
\[ \text{Profit} = 40\% \text{ of CP of B} = 0.40 \times 100 = 40 \]

Thus, the selling price of article B should be:
\[ \text{Selling Price} = 100 + 40 = 140 \]

### Final Answer
The shopkeeper should sell article B for Rs 140 to make a profit of 40%.

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