Question
In a two-digit positive number, the digit in the tens
place is one less than the square of the digit in the units place. Additionally, the difference between the number and the number formed by interchanging the digits is 45. What is 50% of the number obtained by interchanging the digits?Solution
Let units place digit be y and tens place digit be x then, the number will be 10x + y after interchanging the digits we get new number = 10y+x according to question- (10x+y) – (10y+x) = 45 9x- 9y = 45 x-y= 5 and also, x = y^2-1 now, y^2-1-y = 5 y^2- y - 6 = 0 Solving this quadratic equation, we get y = 3, -2 But here negative value in not possible Hence y = 3 And x = 8 New number will be = 10y + x = 38 50% of the number = 19
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