Question

Find the biggest two digit number such that the number is 4 times of the sum of the digits of the number

Answer 1

Let the two digit number be 10a + b
According to the question, 10a + b = 4(a+b)
10a + b = 4a + 4b
6a = 3b
a/b = 1/2

Let a = k and b = 2k (where k is a natural number)
if k = 9 then we get a= 9 and b=18, which is not a 2 digit number.
if k=4 then we get a= 4 and b= 8 (which is a two digit number and is the highest)

therefore the largest such number is 48