CAT 2021 Slot 2 QA Question 12: For a 4-digit number, the sum of its digits in the thousands, hundreds and tens places is 14, the sum of its digits in the hundreds, tens and units places is 15, and the tens place digit is 4 more tha

Question

For a 4-digit number, the sum of its digits in the thousands, hundreds and tens places is 14, the sum of its digits in the hundreds, tens and units places is 15, and the tens place digit is 4 more tha

Accepted Answer

Let the thousands, hundreds, tens and units digits be $a, b, c$ and $d$ respectively.

$a+b+c=14$
$b+c+d=15$
$c=d+4$

Subtract the first equation from the second.
$d-a=1$
$a=d-1$

Using $c = d + 4$ in $a + b + c = 14$,
$(d-1)+b+(d+4)=14$
$b=11-2d$

To maximize the number, maximize the thousands digi