A scientific calculator is available at University Shoppe in Hazratganz at 20% discount and the same is available at only 15% discount at Universal Shoppe Bhootnath Market. Ms. Agrawal has just sufficient amount of Rs. 800 to purchase it at Universal Shoppe Hazratganz. What is the amount that Ms. Agrawal has less than the required amount to purchase it at Universal Shoppe Bhootnath?

Options

A. Rs. 70
B. Rs. 50
C. Rs. 100
D. data insufficient

Answer

To solve the problem step by step, we will first determine the marked price of the scientific calculator based on the information provided about the discounts at both shops.

### Step 1: Determine the Marked Price from University Shoppe
Given that the selling price at University Shoppe (after a 20% discount) is Rs. 800, we can use the formula for selling price:

\[ \text{Selling Price} = \text{Marked Price} \times \left(1 - \frac{d}{100}\right) \]

Where \( d \) is the discount percentage. Here, \( d = 20\% \).

Substituting the values, we have:

\[ 800 = \text{Marked Price} \times \left(1 - \frac{20}{100}\right) \]
\[ 800 = \text{Marked Price} \times \left(1 - 0.2\right) \]
\[ 800 = \text{Marked Price} \times 0.8 \]

### Step 2: Solve for the Marked Price
To find the marked price, we rearrange the equation:

\[ \text{Marked Price} = \frac{800}{0.8} \]
\[ \text{Marked Price} = 1000 \]

### Step 3: Calculate the Selling Price at Universal Shoppe
Now that we have the marked price, we can calculate the selling price at Universal Shoppe, which offers a 15% discount.

Using the same formula:

\[ \text{Selling Price} = \text{Marked Price} \times \left(1 - \frac{d}{100}\right) \]
Where \( d = 15\% \):

\[ \text{Selling Price} = 1000 \times \left(1 - \frac{15}{100}\right) \]
\[ \text{Selling Price} = 1000 \times \left(1 - 0.15\right) \]
\[ \text{Selling Price} = 1000 \times 0.85 \]
\[ \text{Selling Price} = 850 \]

### Step 4: Determine the Amount Ms. Agrawal is Short
Ms. Agrawal has Rs. 800, but the selling price at Universal Shoppe is Rs. 850. To find out how much less she has:

\[ \text{Amount Less} = \text{Selling Price at Universal Shoppe} - \text{Amount Ms. Agrawal has} \]
\[ \text{Amount Less} = 850 - 800 \]
\[ \text{Amount Less} = 50 \]

### Final Answer
Ms. Agrawal is Rs. 50 short of the amount required to purchase the calculator at Universal Shoppe.

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