Question

A two digit number consists of $2$ digits whose sum is $6$. If $18$ is added to the number, its digits are reversed. Find the number.

• A. $24$
• B. $42$
• C. $33$
• D. $15$

Answer 1

The correct option is A $24$

$\text{Let x and y be respectively unit and tenth digit of two-digit number then the number will}$

$10y+x$

$\text{condition 1:the sum of digits is 6 hence}$

$x+y=\mathrm{6........}\left(i\right)$

$\text{condition 2 :when 18 is added to number 10y +x then digits are reversed}$

$i.e$

$18+10y+x=10x+y$

$x-y=\mathrm{2...........}\left(ii\right)$

$\text{adding (i)and (ii) we get}$

$\text{x=4}$

$\text{by putting value of x in (i) or (ii) we get}$

$y=2$

1is added to the number, its digits are reversed. Find the number.}$

$\text{Hence the number is}$

$10y+x$

$=10\times 2+4$

$=24$

$\text{Hence option A is correct.}$