A dealer offered a machine for sale for Rs 27500 but even, if he had charged 10% less, he would have made a profit of 10%, The actual cost of the machine is

Options

A. Rs22000
B. Rs24250
C. Rs22500
D. 22275

Answer

To find the actual cost of the machine, we can follow these steps:

### Step 1: Determine the selling price if the dealer charges 10% less.
The dealer is selling the machine for Rs 27,500. If he charges 10% less, we need to calculate 10% of Rs 27,500 and subtract it from the selling price.

\[ \text{10% of } 27500 = \frac{10}{100} \times 27500 = 2750 \]

\[ \text{Selling Price at 10% less} = 27500 - 2750 = 24750 \]

### Step 2: Use the selling price to find the cost price.
According to the problem, if the dealer sells the machine for Rs 24,750, he would make a profit of 10%. We can use the formula for selling price (SP) which is given by:

\[ SP = CP \times \left(1 + \frac{\text{Profit Percentage}}{100}\right) \]

Where:
- SP = Selling Price (Rs 24,750)
- CP = Cost Price (what we need to find)
- Profit Percentage = 10%

Substituting the values into the formula:

\[ 24750 = CP \times \left(1 + \frac{10}{100}\right) \]

\[ 24750 = CP \times \left(1 + 0.1\right) \]

\[ 24750 = CP \times 1.1 \]

### Step 3: Solve for the cost price (CP).
Now, we can isolate CP by dividing both sides by 1.1:

\[ CP = \frac{24750}{1.1} \]

Calculating this gives:

\[ CP = 22500 \]

### Conclusion
The actual cost of the machine is Rs 22,500.

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