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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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