Question

A man goes to a store to buy a product. The price is in two digits. The shopkeeper mistakenly interchanges the digits and sold it for a new price. If the difference between the original price and the mistake (new) Price is $18, and the sum of the digits is eight. Find the digits.

A. 71
B. 89
C. 26
D. 44

Answer 1

Based on the given information, it is not possible to find the digits of the original price.

Step-by-step explanation:

To solve this problem, let's assume that the original price has two digits: AB. According to the given information, the shopkeeper mistakenly interchanges the digits, so the new price becomes BA. We are told that the difference between the original price and the new price is $18 and the sum of the digits is eight.

From these conditions, we can set up the following equations:

• A - B = 8 (Equation 1)
• 10A + B - (10B + A) = 18 (Equation 2)

We can rewrite Equation 2 as 9A - 9B = 18, which simplifies to A - B = 2 (Equation 3). We can solve Equations 1 and 3 simultaneously to find the values of A and B.

Subtracting Equation 3 from Equation 1, we get:

(A - B) - (A - B) = 8 - 2

0 = 6

Since 0 cannot be equal to 6, this implies that there is no solution to the system of equations. Therefore, it is not possible to find the digits of the original price based on the given information. The correct answer is None of the above options provided (A, B, C, or D).