There is a five digit number. The fourth digit is $4$ greater than the second digit, while the third digit is $3$ less than the second digit. The first is thrice the last digit. The number contains three pairs whose sum is $11$. Find the number.

The correct option is B $65292$
Let five digit number is ABCDE.
$\therefore A=3E.....\left(i\right)$
$D=B+4......\left(ii\right)$
$C=B-3.....\left(iii\right)$
From equation (i), E can be 1, 2 or 3
From equations (ii) and (iii). B can be 3, 4 or 5.
So, A can be $3,6or9$
B can be $3,4$ or $5$
C can be $0,1$ or $2$
D can be $7,8$ or $9$
E can be $1$, $2$ or $3$
Now, sum of three pairs is 11. This condition is satisfied by the number $65292.$