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 het numbers on the removed cards is `k ,` then `k-20=` ____________.

Answer

5

Explanation

Clearly 1+2+3+….+4n-2 `le 1224 lt 3 +4+..n`
`rArr ((n-2)(n-1))/(2)le 1224 lt (n-2)/(2) (3+n)`
`rArr n^2 -3n - 2446 le 0 and n^2+n - 2454 ge 0 `
`n 49 lt n lt 51 rArr n = 50 `
`therefore (n-2)/2-(2k+1)= 1224`
or k = 25
or k- 20 = 5