Ankita sold her text book for a loss of 15%. If she would have sold the textbook for an increased price of Rs 150, there would have been gain of 10%. What was the cost price of the text book?
(a)Rs 500
(b)Rs 900
(c)Rs 400
(d)Rs 600

Options

A. Rs 500
B. Rs 900
C. Rs 400
D. Rs 600

Answer

To find the cost price of Ankita's textbook, we can follow these steps:

### Step 1: Define the Cost Price
Let the cost price (CP) of the textbook be represented as \( x \).

### Step 2: Calculate Selling Price at Loss
Ankita sold the textbook at a loss of 15%. Therefore, the selling price (SP) at this loss can be calculated as:
\[ SP = CP - (15\% \text{ of } CP) = x - 0.15x = 0.85x \]

### Step 3: Calculate Selling Price at Gain
If Ankita had sold the textbook for an increased price of Rs 150, she would have made a gain of 10%. Therefore, the new selling price (SP) can be calculated as:
\[ SP = CP + (10\% \text{ of } CP) = x + 0.10x = 1.10x \]
Since this selling price is also equal to the previous selling price plus Rs 150, we can write:
\[ 0.85x + 150 = 1.10x \]

### Step 4: Solve for x
Now, we can rearrange the equation to isolate \( x \):
\[ 150 = 1.10x - 0.85x \]
\[ 150 = 0.25x \]
To find \( x \), divide both sides by 0.25:
\[ x = \frac{150}{0.25} = 150 \times 4 = 600 \]

### Conclusion
The cost price of the textbook is \( \text{Rs } 600 \).

### Final Answer
Thus, the correct option is (d) Rs 600.

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