Number System
In a two-digit number, if it is known that its unit's digit exceeds its ten's digit by 2 and that the product of the given number and the sum of its digits is equal to 144, then the number is:
Let the two consecutive odd numbers be 2x - 1 and 2x + 1.(2x - 1) (2x - 1) = 4095= 4x² - 1 = 4095= 4x² = 4096= x² = 1024∴ x = 32∴ The numbers are 63 and 65.Greater number = 65
Let the greater and the smaller number be g and s respectively.gs = 2560g + s exceeds g - s by 64 i.e., g + s - (g - s) = 64i.e., 2s = 64 => s = 32.g = 2560/s = 80.
EXAMIANS