Question

a pack contains n cards numbered 1 to n .Two consecutive cards are removed from the pack and sum of remaining card is $1224$.If smaller of number on the removed card is k.Find value of $k-20$

Answer 1

Given

$\frac{n(n+1)}{2}-\left(k\right)-(k+1)=1224$

get $k=n(n+1)-\frac{2450}{4}$

since n should be such that

$n(n+1)>2450$ and

k is integer only $n=50$ satisfies , then

$k=25$ and

$k-20=5$