In a 4-digit number, sum of first two digits is equal to that of last two digits. The sum of first and last digits is equal to third digit. Finally, sum of second and fourth digits is twice sum of or two digits. What is third digit of number?

Let the 1^st, 2^nd, 3^rd and 4^th digits be a, b, c and d respectively.
Then,
a + b = c + d ----------(i)
a + d = c ----------(ii )
b + d = 2(a + c) ----------(iii)
from eqn. (i) and (ii),
a + b = a + 2d
?b = 2d
and eqn (iii);
2d + d = 2(a + a + d)
? 3d = 2(2a + d) ? d = 4a
or, a = $$\frac{{\text{d}}}{4};$$
? Now, from eqn. (ii),
a + d = $$\frac{{\text{d}}}{4}$$ + d = $$\frac{{{\text{5d}}}}{4}$$ = c
Or, c = $$\frac{5}{{4{\text{d}}}}$$
The value of d can be either 4 or 8.
If d = 4, then c = 5
If d = 8, then c = 10
But the value of c should be less than 10
Hence, value of c would be 5