Suppose the digit at unit's places is y and that at ten's places is x.Then, the number = 10x + y,According to the question.x + y = 8 .......(i)Again 10x + y - 18= 10y + x= 10x + y - 10y - x = 18= x - y = 2 ............(iii)From, equation (i) and (iii) we get x + y = 8x - y = 22x = 10= x = 5 and y = 3∴ number = 10 x 5 + 3 = 53
Let the age of the son be x and the age of the father be y.Therefore, x + y = 65 ..........(i)or, 2 x (x + 5) = (y + 5)or, 2x + 10 = y + 5or, 2x - y = 5 ...................(ii)From equations (i) and (ii), x = 20, y = 45
Let 'N' is the smallest number which divided by 13 and 16 leaves respective remainders of 2 and 5.Required number = (LCM of 13 and 16) - (common difference of divisors and remainders) = (208) - (11) = 197.
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