Question

a4c is a three digit number and the sum of its digits is 9. This three digit number is reversed and subtracted from the original number. The difference obtained is 495. Find the number.

• A. 441
• B. 540
• C. 342
• D. 243

Answer 1

The correct option is B 540

Let the given 3-digit number be abc where b = 4.

General form of abc = 100a + 10b + c ... (i)

Number obtained by reversing the digits is cba.

General form of cab = 100c + 10b + a ... (ii)

Subtracting (ii) from (i)
$(100a+10b+c)-(100c+10b+a)$
$=(100-1)a+(10-10)b+(1-100)c$
$=99a-99c$
$=99(a-c)$

Given 99 (a - c) = 495
$\Rightarrow$ a - c = 5
$\Rightarrow$ a = 5 + c ---(i)
and a + 4 + c = 9
$\Rightarrow$ a + c = 5 ----(ii)
Subtitute (i) in (ii)
5 + c + c = 5
$\Rightarrow$ c = 0
We know that, a - c = 5
$\Rightarrow$a = 5

Therefore, the number a4c is 540.