Question

abc is a three digit number such that b = 5 and a - c = 2 . Sum of abc and the number obtained after reversing the digits is 606 . Find the number.

• A. 654
• B. 452
• C. 755
• D. 553

Answer 1

The correct option is B 452

General form of 3-digit number abc = 100a + 10b + c
Number obtained by reversing its digits = cba
General form of cba = 100c + 10b + a

abc + cba
= 100a + 10b + c + 100c + 10b + a
= 101a + 20b + 101c
= 101(a + c) + 20b
= 101(a + c) + 100 [ b = 5]

Given, 101(a + c) + 100 = 706
(a + c) = 606 /101
a + c = 6 and
we also know that a - c = 2

$\Rightarrow$ a + a - 2 = 6
$\Rightarrow$ 2a = 8
a = 4 and c = 2

So the number abc is 452