the sum must be minimized and digits are unique, hence start with the lowest terms for tens and add on digit terms

hope this helps

The solution provided by motion2020 is precise. I'm just trying to elaborate on question

We know ten digits = ( 0,1,2,3,4,5,6,7,8,9)

Let Set S = { 0,1,2,3,4,5,6,7,8,9}

Using the above ten digits we have to form 5 numbers which are between 10 to 99 .SUCH THAT,
i) Each digit in Set S can be used only once.
ii) Sum of the 5 numbers formed should be as low as possible.

So the 5 number satisfying above condition is {10,26,37,48,59}

Now Quantity A = Greatest of the 5 numbers = 59
Quantity B = 60

Therefore Quantity A < Quantity B
Hence answer is option B

Note that the sum of these 5 numbers should be as low as possible, therefore make pairs of the smallest digit with the largest digit. Thus, we have 1 with 0 (as the question allows inclusion of 10), 2 with 9 =29, 3 with 8=38, 4 with 7 =47 and 5 with 6 =56. The logic behind pairing largest digits with the smallest is that that shall ensure our sum is smallest. The set is {10, 29, 38, 47, 56} and sum is 180. The above set also gives the sum 180 but this logic saves time from forming random sets. Hope this explains why people have solved in the manner above