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if it is a number between 300 and 400 and if it is even then it would be between
302-398.
In which case, we've already identified the number in the hundreds place as 3.
the number would be
3xy
x being the digit in the tens place and y in the units place
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if the sum of the digits is five times the hundred digit then
3+x+y = 5(3)
3+x+y =15
x + y = 15 - 3
x + y = 12
that being x + y = 12, we can have investigation through trial and error
we'll have:
3xy
since it is even then we'll base the assumptions in its units digit
if y = 0
x = 12
not correct since we can't have two digits for the tens place
if y = 2
x = 10
not correct with same reason as the first
if y = 4
x = 8
can be since it qualifies to the condition that no digit shall be the same as the other
if y = 6
x = 6
doesn't satisfy the 'I have three different digits' statement
if y = 8
x = 4
can be
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so the number can either be
348 or 384