An almirah was sold at a profit of 15%. If its cost had been 5% less and it had been sold for Rs 1,470 less, then the profit would have been 10%. What is the cost price of the almirah?

Options

A. Rs,14,000
B. Rs,29,000
C. Rs, 16,100
D. Rs ,2,94,000

Answer

To find the cost price of the almirah, let's denote the cost price as \( x \).

1. **Calculate the selling price at 15% profit:**
The selling price (SP) when sold at a profit of 15% is given by:
\[ SP = x + 0.15x = 1.15x \]

2. **Determine the new cost price if it were 5% less:**
If the cost price is 5% less, the new cost price will be:
\[ \text{New Cost Price} = x - 0.05x = 0.95x \]

3. **Selling price if sold for Rs 1,470 less:**
If the almirah is sold for Rs 1,470 less, the new selling price would be:
\[ \text{New Selling Price} = 1.15x - 1470 \]

4. **Set up the equation for 10% profit:**
If the new selling price results in a profit of 10%, we can express this as:
\[ \text{New Selling Price} = \text{New Cost Price} + 10\% \text{ of New Cost Price} \]
Therefore,
\[ 1.15x - 1470 = 0.95x + 0.10(0.95x) \]
Simplifying the right side:
\[ 0.10(0.95x) = 0.095x \]
Thus,
\[ 1.15x - 1470 = 0.95x + 0.095x \]
\[ 1.15x - 1470 = 1.045x \]

5. **Rearranging the equation:**
Now, we rearrange the equation to isolate \( x \):
\[ 1.15x - 1.045x = 1470 \]
\[ 0.105x = 1470 \]

6. **Solve for \( x \):**
Dividing both sides by 0.105 gives:
\[ x = \frac{1470}{0.105} = 14000 \]

Thus, the cost price of the almirah is Rs 14,000.