A no consists of 2 digits whose product is 18 when 27 is subtracted from the no the digit inter change find the number
the digits are a,b
a*b = 18
10a+b - 27 = 10b + a
a=6 b=3
check:
63 - 27 = 36
To find the number, let's break down the problem step by step.
1. Start with a two-digit number: Let's represent this number as "xy", where "x" represents the tens digit and "y" represents the ones digit.
2. The product of the two digits is 18: This gives us the equation x * y = 18.
3. When 27 is subtracted from the number, the digits interchange: Mathematically, this can be written as (10x + y) - 27 = (10y + x).
To solve the problem, we'll use the following steps:
Step 1: From the equation x * y = 18, we need to list all possible combinations of two digits that multiply to give 18. Those combinations are (1, 18), (2, 9), and (3, 6).
Step 2: We'll substitute each combination into the equation (10x + y) - 27 = (10y + x) and solve for x and y. Let's go through each combination:
- For (1, 18):
(10 * 1 + 18) - 27 = (10 * 18 + 1) -> 28 - 27 = 181 -> 1 = 181 (not true)
- For (2, 9):
(10 * 2 + 9) - 27 = (10 * 9 + 2) -> 29 - 27 = 92 -> 2 = 92 (not true)
- For (3, 6):
(10 * 3 + 6) - 27 = (10 * 6 + 3) -> 36 - 27 = 63 -> 9 = 63 (not true)
Since none of the combinations satisfy the equation, there is no valid solution to the problem.