Question

A three digit number is such that the ten’s digit is two more than the hundred’s digit and two less than the unit’s digit. If the number is increased by nine and the result divided by the sum of the original digits, the quotient is . Find the number.

Answer 1

Let the digits of the number be a, b and c, such that the number

N= 100a+10b+c

Digit in the unit’s place is twice the digit in the ten’s place

c = 2 x b

b= (c/2) —(1)

Digit in the unit’s place is 1.5 times the digit in the hundred’s place

c = 1.5 x a

a= (2/3) c —(2)

sum of all the three digits of the number is 13

a+b+c = 13 —-(3)

(2/3)c + (c/2) +c = 13

c= 6

b=3 ; a = 4

N=1004+ 10 x 3+ 6= 436

Ans: The number is 436