A pack contains `n` cards numbered from 1 to `n` . Two consecutive numbered cards are removed from the pack and the sum of the numbers on the remaining cards is 1224. If the smaller of the numbers on the removed cards is `k ,` then `k-20=` ____________.

Explanation

Let two consecutive nymbers are k and `k+1` such that `1leklen-1`, then
`(1+2+3+"……."+n)-(k+k+1)=1224`
`implies (n(n+1))/(2)-(2k+1)=1224" or " k=(n^(2)+n-2450)/(4)`
Now, `1le (n^(2)+n-2450)/(4) le n-1 implies 49ltnlt51`
`:. n =50 implies k=25`
Hence, `k-20=25-20=5`.