Learn
If a certain number of two digits is divided by the sum of its digits, the quotient is 6 and the remainder is 3. If the digits are reversed and the resulting number is divided by the sum of the digits, the quotient is 4 and the remainder is 9. The sum of the digits of the number is ?
8
6
9
12
14
8
6
9
12
14
Solution
Let the two digits number be = ab
Therefore ab = 10a + b
Sum of the digits = a + b
Therefore,
10a + b = (a + b)6 + 3
10a + b = 6a + 6b + 3
4a − 5b = 3 —– (1)
The resulting number when the digits are reversed is = ba
ba = 10b + a
10b + a = (b + a)4 + 9
10b + a = 4b + 4a + 9
6b − 3a = 9 —– (2)
Adding Eq (1) and (2) we get
a + b = 12
The sum of the digits of the number is = 12
Register & Unlock access to Prep for free
Solution
Keynote
A two digit number ‘ab’ can be written as 10a +b.
Example: 36 = 3(10) + 6
Similarly a three digit number ‘abc’ can be written as 100a + 10b + c.
Example: 256 = 2(100) + 5(10) + 6
