Q.
A three digit number abc is such that
(i) its hundreds digit is equal to the sum of the other two digits, and
(ii) $b(c + 1) = 52 - 4a$
Number of such numbers are
Permutations and Combinations
Solution:
$N = abc $
$a = b + c$
$b(c + 1) = 52 - 4a$
$b(c + 1) = 52 - 4(b + c)$
$bc + b = 52 - 4b - 4c$
$bc + 5b + 4c + 20 = 52 + 20$ (add 20 on both sides)
$(b + 4)(c + 5) = 72$
