Question

A salesman enters the quantity sold and the price into the computer. Both the numbers are two-digit numbers. But, by mistake, both the numbers were entered with their digits interchanged. The total sales value remained the same, i.e. Rs. 1,148, but the inventory reduced by 54. What is the actual price per piece?

• A. Rs. 82
• B. Rs. 41
• C. Rs. 6
• D. Rs. 28

Hint:

Digit reversal problems often involve forming expressions using 10a + b and logical assumptions.

Answer 1

The Correct Option is B

Step 1: Let the actual quantity = 10a + b and price = 10c + d
Step 2: Due to interchange, the entered quantity = 10b + a and price = 10d + c
Step 3: Actual value = Entered value = Rs. 1,148
(10a + b)(10c + d) = (10b + a)(10d + c) = 1148
Step 4: The inventory dropped by 54, so:
(10a + b) − (10b + a) = 54 ⇒ 9a − 9b = 54 ⇒ a − b = 6
Step 5: Try small values: a = 8, b = 2 ⇒ quantity = 82, entered quantity = 28
Step 6: Check: 82 × x = 1148 ⇒ x = 1148 ÷ 82 = 14
Step 7: Reverse: 28 × y = 1148 ⇒ y = 41
Step 8: So actual price = Rs. 41