Yogita sold a plasma TV at 20% gain to Shyamla. Shyamla sold It to Deepa at 10% profit. If Deepa ad to pay 33,000 for the plasma TV, find the cost price of the plasma TV for Yogita.

Options

A. 30000
B. 25000
C. 35000
D. 40000

Answer

To find the cost price of the plasma TV for Yogita, we can follow these steps:

### Step 1: Understand the Selling Prices and Profit Percentages
Yogita sells the TV to Shyamla at a 20% gain. This means that if Yogita's cost price (CP) is \( x \), then the selling price (SP) for Yogita is:
\[ SP_{Yogita} = CP + 20\% \text{ of } CP = x + 0.2x = 1.2x \]

### Step 2: Shyamla's Selling Price
Shyamla sells the TV to Deepa at a 10% profit. Therefore, if Shyamla's cost price is the same as Yogita's selling price, then:
\[ SP_{Shyamla} = CP_{Shyamla} + 10\% \text{ of } CP_{Shyamla} = 1.2x + 0.1(1.2x) = 1.2x + 0.12x = 1.32x \]

### Step 3: Set Up the Equation with Deepa's Price
We know that Deepa pays ₹33,000 for the TV. Therefore, we can set up the equation:
\[ 1.32x = 33,000 \]

### Step 4: Solve for Yogita's Cost Price
To find \( x \), we divide both sides of the equation by 1.32:
\[ x = \frac{33,000}{1.32} \]

Calculating this gives:
\[ x = 25,000 \]

### Conclusion
Thus, the cost price of the plasma TV for Yogita is ₹25,000.

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