Number System
The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and 15 as remainder. What is the smaller number?
Let the middle digit be x. Then, 2x = 10 or x = 5.So, the number is either 253 or 352. Since the number increases on reversing the digits, so the hundred's digit is smaller than the unit's digit. Hence, required number = 253.
Since the difference between the divisors and the respective remainders is not constant, back substitution is the convenient method. None of the given numbers is satisfying the condition.
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
EXAMIANS