Question

the sum of three digit number is 15. the digit at the tens place is half of the sum of the digit at hundred and unit place. if 396 is added to the number, the digit at the hundred and unit place are interchange. Find the number?

Answer 1

x+y+z=15 (given)
$y = \frac{x + z}{2}$
x+z=2y
Substituting this in the given equation.
3y=15
y=5
Now,
x+z=10 using the formula x+z=2y.
Now the main part.
The three digit number can be written as
100x+10y+z.
According to them, 100x+10y+z+396=100z+10y+x.
Solving this you'll get
99x-99z=-396
that is x-z=-4
but x+z=10
Solving these two equations we get,
x=3 and z=7
Therefore the required number is 357.
Verification:-
357+396=753.

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