On selling a book at `9/14` of the marked price, there is loss of 10%. What will be the ratio of marked price and cost price of the book?

Options

A. `5:9`
B. `5:8`
C. `7:4`
D. `7:5`

Answer

To solve the problem step by step, we will denote:

- Marked Price (MP) = M
- Cost Price (CP) = C
- Selling Price (SP) = S

Given:
1. Selling Price (S) = \( \frac{9}{14} \) of the Marked Price (M)
2. There is a loss of 10%.

### Step 1: Express Selling Price in terms of Marked Price
From the information given, we can express the Selling Price (S) as:
\[ S = \frac{9}{14} M \]

### Step 2: Understand the Loss Percentage
A loss of 10% means that the Selling Price is 90% of the Cost Price. Therefore, we can write:
\[ S = C - 0.10C = 0.90C \]

### Step 3: Set the two expressions for Selling Price equal
Now we have two expressions for Selling Price:
\[ \frac{9}{14} M = 0.90C \]

### Step 4: Rearranging the equation to find the ratio of Marked Price to Cost Price
To find the ratio of Marked Price (M) to Cost Price (C), we can rearrange the equation:
\[ M = \frac{0.90C \cdot 14}{9} \]
\[ M = \frac{12.6C}{9} \]
\[ M = \frac{14C}{10} \]

### Step 5: Find the ratio of Marked Price to Cost Price
Now we can find the ratio of Marked Price (M) to Cost Price (C):
\[ \frac{M}{C} = \frac{14}{10} = \frac{7}{5} \]

### Conclusion
Thus, the ratio of Marked Price to Cost Price is:
\[ \text{Ratio of Marked Price to Cost Price} = 7:5 \]

---