The marked price of a book is Rs. 4200. The shopkeeper gives two successive discounts of 25% and y% to the customer. If the customer pays Rs. 2898 for the book, what is the value ( in per cent) of y ?

Options

A. 7
B. 8
C. 6
D. 5

Answer

To solve the problem step by step, we will calculate the successive discounts and find the value of \( y \).

### Step 1: Calculate the first discount
The marked price of the book is Rs. 4200, and the first discount is 25%.

First, we calculate the amount of the first discount:
\[ \text{First Discount} = \frac{25}{100} \times 4200 = 1050 \]

### Step 2: Calculate the price after the first discount
Now, we subtract the first discount from the marked price to find the price after the first discount:
\[ \text{Price after first discount} = 4200 - 1050 = 3150 \]

### Step 3: Set up the equation for the second discount
The customer pays Rs. 2898 after both discounts. Let \( y \) be the percentage of the second discount. The selling price after the second discount can be expressed as:
\[ \text{Selling Price} = \text{Price after first discount} - \text{Second Discount} \]
This means:
\[ 2898 = 3150 - \left( \frac{y}{100} \times 3150 \right) \]

### Step 4: Solve for the second discount
Rearranging the equation gives us:
\[ \frac{y}{100} \times 3150 = 3150 - 2898 \]
Calculating the right side:
\[ 3150 - 2898 = 252 \]
So we have:
\[ \frac{y}{100} \times 3150 = 252 \]

### Step 5: Isolate \( y \)
Now, we can isolate \( y \):
\[ y = \frac{252 \times 100}{3150} \]

### Step 6: Calculate \( y \)
Calculating the value of \( y \):
\[ y = \frac{25200}{3150} = 8 \]

Thus, the value of \( y \) is:
\[ y = 8\% \]

### Final Answer:
The value of \( y \) is 8%.

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