Number System
The difference between a two-digit number and the number obtained by interchanging its two digits is 45. The sum of the digit of the number is 9. What is the product of the two digits of the number?
Let the number be 10x + y.Therefore, x + y = 9 ..................(i)10x + y - (10y + x) = 4510x + y - 10y - x = 45Therefore, x - y = 5 ..................(ii)From (i) and (ii), x = 7, y = 2Number = 72Therefore, = x x y = 7 x 2 = 14
Let the consecutive even numbers be A = 2x, B = 2x + 2, C = 2x + 4, D = 2x + 6 and E = 2x + 8= A + B + C + D + E = 130= 10x + 20 = 130∴ x = 130 - 20/10 = 11Therefore, product of A and E= 22 x 30 = 660
Let the present age of the father be 'x' and that of the son be 'y'. Then x/y = 8/3∴ 3x = 8y Further, x + 12/y + 12 = 2/1 ∴ x + 12 = 2y + 24 ∴ x - 2y = 12 ......(ii)From eqn (i) and (ii), x = 48, y = 18 ∴ sum = 66 yrs.
EXAMIANS