Number System
The difference between a two-digit number and the number obtained by interchange the two digits of the number is 27. If the sum of the two digits of the number is 13, what is their product ?
Let the number be 10x + y.∴ 10x + y - (10y + x) = 27or 9x - 9y = 27∴ x - y = 3 .......(I)x + y = 13 .......(II)From eqn (I) and (II)x = 8 and y = 5.So the number = 85Therefore, product = 8 x 5 = 40
Since the number is greater than the number obtained on reversing the digits, so the ten's digit is greater than the unit's digit.Let the ten's and unit's digits be 2x and x respectively.Then, (10 * 2x + x) - (10x + 2x) = 369x = 36x = 4Required difference = (2x + x) - (2x - x) = 2x = 8.
Let the numbers be x, x + 2, x + 4, x + 6, and x + 8Avg = x + x + 2 + x + 4 + x + 6 + x + 8/5 = 40Therefore, 5x + 20 = 200Therefore, x = 180/5 = 36Therefore, r = x + 4 = 40 s = x + 6 = 42Therefore, Product = 1680
EXAMIANS